COOBER PEDY, Australia — A few weeks ago, Deb Williams saw another dead kangaroo lying in the middle of the Stuart Highway, a strip of road almost 2,000 miles long that runs north-south through Australia’s center.

So she did what she normally does. She slowed her car down from 70 miles an hour and pulled over to drag the lifeless animal off the road. As a nurse, Ms. Williams, 50, has seen firsthand the effects that hitting kangaroos has on drivers. From the smell and site of the carcass, she estimated it had been there for a few days, all life long gone. Or so she thought.

“When I looked at the kangaroo, I saw movement and I thought, ‘You’ve got to be kidding me, there cannot be a joey in there,’” Ms. Williams recalled, referring to a baby kangaroo. Once the body was off the road, she peeked into the pouch to find the baby, covered in its mother’s blood, but almost unscathed and very much alive.