Heard was charged Tuesday with two counts of illegally importing the pups, Pistol and Boo, into the country and one count of producing a false document, a spokesman for the Commonwealth Department of Public Prosecutions confirmed to PEOPLE.
She has been issued a summons to appear at the Southport Magistrates Court in Queensland on Sept. 7.
The importation charges could lead to a maximum penalty of 10 years in prison and a fine of $75,000. The false document charge carries a penalty of up to a year in prison and a fine of $7,500.
Heard's legal representation can petition the court to appear on her behalf, Brisbane-based criminal defense attorney Bill Potts, explained to the Associated Press on Wednesday. But given the seriousness of the charge, the actress may be required to appear in person.
Potts also told the news outlet that the 29-year-old is unlikely to face a lengthy jail term because the pets were returned to the United States before the 72-hour deadline issued by Aussie politician Barnaby Joyce back in May.
Heard and the Pirates of the Caribbean star, 52, first encountered the legal trouble Down Under when they failed to declare the animals to customs authorities when they arrived in Brisbane via private jet in April. Joyce then threatened to euthanize the dogs if the couple did not remove them from Australia within a 72-hour window. (Australia requires dogs to be quarantined for at least 10 days upon entering the country. )
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Joyce, the Australian Minister for Agriculture, told the Sydney Morning Herald that authorities found out about the dogs "because we saw him taking them to a poodle groomer. Now, Mr. Depp has to either take his dogs back to California or we're going to have to euthanize them."
The politician went on, "Just because he's Johnny Depp does not mean he's exempt from Australian law... You start letting in movie stars, even though they have been the Sexiest Man Alive twice, who come into our nation, why don't we just break the laws for everybody?"
The dogs were then put on a private jet back to the U.S. within the timeframe and Depp remained in Australia to continue filming Pirates of the Caribbean: Dead Men Tell No Tales.
Heard told Australia's Channel 7 News last month, "I have a feeling we're going to avoid the land Down Under from now on, just as much as we can, thanks to certain politicians there. I don't know, I guess everybody goes for their 15 minutes, including some government officials."
Depp has not commented publicly on the matter.