(CNN) The Internet is a dangerous place for Mariam Veiszadeh right now. It's where death threats lurk and vile messages appear faster than they can be deleted.

But it's also a place where support is growing in a Twitter counter-campaign -- #IStandWithMariam -- to the urgings of a U.S.-based white supremacist website, the Daily Stormer, to "be as nasty, hurtful, hateful, offensive, insulting and 'vilifying' as you possibly can."

And they have been. "Leave now before we behead your mother and bury you all with pigs..." said one tweet from an account, which has since been suspended. Many of the messages include extremely offensive hashtags.

Veiszadeh, an Australian lawyer and founder of the Islamophobia Register , which tracks instances of abuse against Muslims, knows exactly why she's being targeted.

"The reality is people don't abuse me just because I'm a woman or because my name is Mariam or because I'm Middle-Eastern. They abuse me because I have a scarf on my head and because I'm a Muslim," Veiszadeh told CNN.

It started with a tweet over a T-shirt

Last October, Veiszadeh posted an image of a T-shirt for sale in Woolworths, one of Australia's biggest retailers, which showed the Australian flag with the words "If you don't love it, leave."

She called the shirt "bigoted," a flood of complaints followed and the shirt was withdrawn from sale. Woolworths apologized and blamed an ordering error, saying it "should never have been on our shelves."

Pls RT @woolworths I'm outraged that #WOOLWORTHS are allegedly selling these bigoted singlets at their Cairns stores pic.twitter.com/0GVwscbpuK — Mariam Veiszadeh (@MariamVeiszadeh) October 13, 2014

That could have been the end of it.

However, three months later, the Australian Defence League (ADL) -- a right-wing group that's calling for Islam to be banned in Australia -- posted Veiszadeh's tweet on its Facebook site, along with another one she posted saying "Everyone is entitled to dress as they please," with the title "Hypocrisy Much?"

The post attracted dozens of offensive comments. Abusive tweets followed but the campaign took a more sinister -- and organized -- twist when the Daily Stormer implored its "troll army" to attack her.

The post, in part, justifies the attack as revenge for the prosecution of a 22-year-old woman from Ipswich , in the Australian state of Queensland. The woman allegedly sent a stream of invective to Veiszadeh, calling her a tramp, whore, "rag head" and other offensive names.

She's been charged with "using a carriage service to menace, harass or cause offense" and is due to appear on court on March 11.

Defending free speech?

On the blog post calling for the tirade of abuse, the Daily Stormer publisher justifies the attack by saying attempts to ban freedom of speech "should be responded to with the most ridiculous conceivable hateful speech."

It recalls a similar "successful" campaign against Luciana Berger , a British MP who was targeted with a barrage of abusive messages after a man was jailed for sending her an anti-Semitic tweet.

"The goal of these operations is to purposefully enrage the target, so as to escalate the situation to the level of media attention, and the method for doing that is through the most extreme speech possible," writes Daily Stormer publisher Andrew Anglin on one blogpost.

He said attention would force a discussion about whether people should be jailed for hate speech, concluding that "the vast majority of White (sic) people do not think name-calling should be an imprisonable offense."

I will not be silenced

Veiszadeh is adamant the campaign of intimidation will not be successful. "If their stated objective is to silence me, then my stated objective is to do the exact opposite," she said.

All the way from US of A. You go girl. #IStandWithMariam — Hana Khan (@hana_khan99) February 25, 2015

Earlier this week, Australian Prime Minister Tony Abbott foreshadowed tougher penalties for hate speech, as part of a move to strengthen the country's counter-terrorism laws. "No one should make excuses for Islamist fanatics or their imitators here in Australia," Abbott said.

Australia's Race Discrimination Commissioner Tim Soutphommasane -- who himself has been the target of a Daily Stormer hate campaign -- says the country's current laws under the Racial Discrimination Act "send an important message to bigots and racists."

"Those who peddle messages of hatred should be made to answer for their extremism. And they should know that the rest of Australian society rejects their promotion of fear and division," he said.

Taking on trolls

However, the Racial Discrimination Act does not cover attacks on a person based on their religious beliefs. That's covered by state laws, which vary from state to state. Veiszadeh said in New South Wales, where most of Australia's Muslims live, there's no law to cover Muslims who are abused on the basis of their religion.

Of the Queensland woman due to face court, Veiszadeh said, "Had this woman not referred to my ethnicity, I would have absolutely no grounds to take action against her."

But even a change in Australian law wouldn't solve the issue of attacks emanating from outside the country by trolls who create multiple fake accounts to attack then vanish. The Daily Stormer has issued instructions to its followers on exactly how to do it, reminding them not to threaten violence (though some have), presumably in an attempt to avoid legal action.

Right now, Veiszadeh is concentrating on naming the trolls and urging her 15,000 followers to block their accounts.

"I'm still getting horrifying images and abusive tweets but, as bad as that sounds, I've become accustomed to it. I've developed a thick skin and for me it's about exposing bigotry and raising awareness about Islamophobia."