Prosecutors dropped two more serious charges that Heard, who is married to actor Johnny Depp, illegally imported the Yorkshire terriers, Pistol and Boo, into the country last year, when Depp was filming the fifth movie in the Pirates of the Caribbean series.
A conviction on the illegal importation counts could have sent the actress to prison for up to 10 years.
The false documents charge carries a maximum penalty of a year in jail and a fine of more than A$10,000 (€6,800), but magistrate Bernadette Callaghan sentenced Heard instead to a one-month good behaviour bond.
The condition means she will have to pay a A$1,000 fine if she commits any offences in Australia over the next month.
Depp and Heard said little to the waiting throng of reporters and fans outside the Southport Magistrates Court on Queensland state’s Gold Coast, but did submit a videotaped apology to the court that was played during the hearing.
“When you disrespect Australian law,” a grim-looking Depp says in the video, “they will tell you firmly.”
The drama over the dogs began last May, when agriculture minister Barnaby Joyce accused Depp of smuggling the tiny terriers aboard his private jet when he returned to Australia to resume filming the movie.
Australia has strict quarantine regulations to prevent diseases such as rabies from spreading to its shores.
Bringing pets into the country involves applying for a permit and quarantine on arrival of at least 10 days.
“If we start letting movie stars — even though they’ve been the sexiest man alive twice — to come into our nation [with pets], then why don’t we just break the laws for everybody?” Mr Joyce said at the time.
“It’s time that Pistol and Boo buggered off back to the United States.”
Depp and Heard were given 72 hours to send Pistol and Boo back to the US, with officials warning the dogs would otherwise be euthanised. The pooches boarded a flight home just hours before the deadline ran out.
The comments by Mr Joyce, who is now deputy prime minister of Australia, elevated what might otherwise have been a local spat into a global delight for comedians and broadcasters.
One newspaper ran a doggie death countdown ticker on its website that marked the hours remaining before the dogs had to flee the country, and comedian John Oliver dedicated a more than six-minute segment to lampooning the ordeal.
Depp himself poked fun at the drama during a press conference in Venice last year where he was asked if he planned to take the dogs for a gondola ride.
“No,” he replied. “I killed my dogs and ate them, under direct orders from some kind of, I don’t know, sweaty, big-gutted man from Australia.”
Mr Joyce posted a link to the couple’s apology video on his Facebook page, and told reporters he doubted it was something the pair would have “willingly wanted to do”.
Still, he gave them credit for acknowledging they made a mistake.
“I am happy Ms Heard has admitted she was wrong and, as such, that clearly shows that our position in pursuit of this was correct,” he told journalists.
“Every nation has something that they’re red hot about, and we’re red hot about our biosecurity requirements in this nation.”