Heard was charged in July with two counts of illegally importing the dogs into the country and one count of producing a false document to quarantine officials.
She could face up to 10 years in prison and heavy fines if convicted.
In a statement, Heard said she instructed her lawyer to plead not guilty, and that she would come to Australia to fight the charges in a trial next year on a date yet to be set.
“My decision to defend these charges, as will become apparent in the appropriate forum of the Court, is not intended to in any way diminish the importance of Australia’s laws,” she said.
The Gold Coast Bulletin newspaper said her lawyer had asked the trial date be moved up from an available date in March.
The pair’s legal team would not say whether Depp would also attend the court for the trial, the newspaper reported.
Heard did not appear at the Southport Magistrates Court in Queensland state on Monday for the latest hearing.
A court official, who would not be quoted by name because of government policy, said the case was adjourned until December 15.
The official could not comment on what else had taken place during Monday’s court hearing.
Australia imposes 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.
Heard is accused of illegally bringing her dogs into Australia on a private jet when she visited Depp, who was filming the latest Pirates of the Caribbean movie on the Gold Coast.
Heard’s lawyer Paula Morreau did not immediately respond to a request for comment.