San Franciscans know they’ll see all walks of life along Market Street, but a new fixture on the colorful thoroughfare has shocked even the most hardened city dwellers: a 6-week-old, homeless baby girl.

All day long, Megan Doudney, 34, sits on the sidewalk near the Four Seasons Hotel between Third and Fourth streets with little Nedahlia in her arms and a sign reading, “Anything helps.” The sight is alarming, even in this city where just about anything goes.

Pedestrians walking past do double takes, exclaiming, “Oh my God!” or “She has a baby!” But they’re not on some hidden-camera show. This is very much real life.

Several people have called 911, including when another homeless person’s menacing dog got in the baby’s face. Police have responded numerous times, and child welfare workers from the Human Services Agency have investigated whether the baby should be removed from Doudney. At first blush, it seems obvious that’s the right answer, but so far, the city is throwing up its hands. Apparently, the newborn is healthy and developing well, and isn’t going anywhere.

“I’m not harming her in any way,” Doudney told me as we chatted on the sidewalk the other day.

She held the sleeping baby, who was wrapped in a fluffy blue blanket. She noted a medical checkup required by the child welfare workers a couple of weeks ago found the baby had low blood sugar but was otherwise fine. And what if the city did try to remove the baby?

“They’d have a fight on their hands — a serious, serious fight,” said Doudney, who sports short blue dreadlocks. “I love her. I wanted my entire life to be a mommy. Even when I was a little kid in school, they’d say, ‘What do you want to be when you grow up?’ I always said, ‘A mommy.’”

Now she is one. But should she be? At least while she’s on the streets? Like everything about the city’s homeless problem, there is no easy answer.

Doudney and her baby have a private room at Hamilton Family Shelter, where they sleep every night and have access to three meals a day and parenting classes. The room is hers for three to six months, and she’s working with a case manager to figure out what comes next. Doudney receives $900 a month in Social Security benefits, and Hamilton sets aside 75 percent of that to save for her future.

Doudney said she needs more than the remaining $225 a month to afford diapers, formula, clothes and other necessities — and that she must panhandle every day to get it.

Rachel Kenemore, development and communications manager at Hamilton, said Doudney is keeping all her appointments with her case manager and that “she seems to be really caring and capable.”

She said staff has no concerns about the baby’s health.

“We have just felt a lot of empathy for Megan,” Kenemore said. “It’s hard to see folks throwing blame instead of looking at this from a compassionate viewpoint of ‘What can we do to ensure this isn’t happening?’”

Chandra Johnson, spokeswoman for the Human Services Agency, wouldn’t discuss Doudney’s specific case, for confidentiality reasons. But she said that, in general, a baby remains with his or her parent unless there is abuse, neglect or failure to develop.

“It’s really important to remember that being homeless alone is not a reason that our agency would remove a child from a family,” she said.

Logically, that seems right. In the heart and in the gut, though, there’s still something wrong about seeing a newborn baby on Market Street all day as her mother panhandles. Doudney has clearly made a string of bad decisions. And if the city can’t compel her to make different choices, its outreach workers should at least attempt to coax her into placing her baby in day care on the city’s dime. The city offers subsidies for homeless families to find free day care for their children so they can work or otherwise get their lives in order.

That kind of help would be more effective than the shaming some passersby on Market Street have tried. Doudney’s image has been splashed all over social media and Next Door email lists, the jaw-dropping pictures of a homeless baby shared like selfies.

The story got even more stomach-churning earlier last week when a North Beach artist spent hours standing over Doudney holding a big pink sign reading, “Women Against Child Abuse!” and followed her for blocks after the homeless mother moved on. Doudney is adamant that she’s not exploiting her child and that she shouldn’t be treated like a freak show just because she’s destitute.

“I am human,” she said. “You can stop and talk to me. You don’t have to shake your head and give me dirty looks.”

When asked about herself, Doudney was candid, coherent and friendly. She said she grew up in a poor family in Fremont, Neb., graduated from high school and attended cosmetology school. Scoliosis and chronic back pain led her to become hooked on opioids.

She said she came to San Francisco on a Greyhound bus five years ago seeking medical marijuana for her pain and that she now uses no hard-core drugs. She does smoke cigarettes heavily, though. She said she has been diagnosed with depression and has had suicidal tendencies in the past, but is doing better. She still talks to family in Nebraska sometimes, but doesn’t want to go back there.

She said she dated a guy for a couple of months — “long enough to get pregnant” — before he became abusive. He’s not in her life and not paying child support. Doudney was sleeping on the streets while pregnant, but received help from the Homeless Prenatal Program and got into a shelter just before giving birth at St. Luke’s Hospital. City officials would not verify Doudney’s story.

Martha Ryan, executive director of Homeless Prenatal, said it’s very rare to see a homeless mother be so public with her baby. But she said there are many more like Doudney. She said in the last month alone, her nonprofit helped 32 women who are homeless and pregnant in San Francisco. The group recently encountered a mother living in her car with a 2-week-old.

“I don’t like to see them on the streets panhandling, but what are you going to do?” Ryan said. “You can’t penalize a mother because she is homeless and living in a shelter and have her baby taken away.”

Doudney’s only friend in San Francisco is Efrem Bryan, a 54-year-old homeless man who is almost always sitting next to her in his wheelchair. They met within hours of her arrival at the Transbay Terminal five years ago and have been inseparable since.

“She’s taking beautiful, great care of the child,” he said, adding he doesn’t understand why the mom and baby have sparked such a fuss. “I thought this was America. I thought this was the land of the free.”

Doudney is vague about her future plans, but said she wants to be off the streets by the time her baby can remember things. And as for her dreams for her girl?

“I just want her to be happy,” she said. “That’s it.”

San Francisco Chronicle columnist Heather Knight appears Tuesdays and Sundays. Email: hknight@sfchronicle.com Twitter: @hknightsf