However, the actress has had two other, more serious charges of illegally importing the terriers Pistol and Boo into the country dismissed.
A conviction on the illegal importation counts could have sent Heard to prison for up to 10 years.
The false documents charge carries a maximum penalty of a year in jail and a fine of over $10,000 Australian dollars.
Heard arrived at Southport Magistrates’ Court in Queensland state today with her husband Depp amid a media scrum.
The couple were swarmed by reporters when they arrived in a black limousine.
They said little apart from Depp responding “Fine, thank you,” to reporters shouting questions about how Pistol and Boo were doing.
Twelve witnesses have been listed to give evidence but it is unclear whether Depp will be called on.
The hearing was briefly adjourned to allow the judge time to review documents, but has now resumed.
The case, dubbed the “war on terrier”, began in May last year when Agriculture Minister Barnaby Joyce accused Depp of sneaking the terriers aboard his private jet when he returned to Australia for the filming of Pirates of the Caribbean: Dead Men Tell No Tales
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 that the dogs would otherwise be euthanised. The pooches boarded a flight home just hours before the deadline ran out.
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