The celebrity couple arrived in Australia last May aboard a private jet, with Depp in the country to film a 'Pirates of the Caribbean' movie.
Depp was not charged over the incident but accompanied his wife to appear at the Southport Magistrates Court on the Gold Coast where they received a red carpet-like reception.
The two were besieged by media although police were on hand to keep things under control.
Heard's defense team described the Pistol and Boo "saga" as a "tired, terrible mistake."
The actress said she was "distracted" when filling out the immigration forms upon her arrival however the prosecution countered that it was "no excuse" -- Australia's famously strict biosecurity law "applies to everyone."
Heard also made a video apology that was heard by the court in which she recognized that it is a "serious crime."
The illegal import of animals carries a maximum penalty of 10 years in prison and a fine of 102,000 Australian dollars ($75,000); the false document charge has a maximum penalty of a year in prison and a fine of 10,200 Australian dollars ($7,500).
Sentencing is expected Monday afternoon.
War on Terrier
The incident gained international attention when Australian Agriculture Minister Barnaby Joyce threatened to have the dogs put down.
"Mr. Depp needs to take his dogs back to California, or we're going to have to euthanize them," Joyce said.
The couple was given a 72-hour ultimatum to get the dogs out of the country.
The Depps quickly returned to California but not before sparking the hashtag #WaronTerrier.
Source → Johnny Depp's wife in court for dog smuggling trial