Matthew and Grace Huang were originally jailed in January 2013 and faced charges of murder following the death of their daughter, Gloria.
They were released from prison last November, but were banned from leaving Qatar during their trial.
A court in the natural gas-rich OPEC nation sentenced the California couple to three years behind bars on March 27.
The Huangs say their adopted daughter, who was born in Ghana, died of medical problems complicated by unusual eating habits that included periods of binging and self-starvation.
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Defense witnesses have testified that the girl appeared healthy and active just days before her death.
Lawyers for the couple have vowed to appeal the case, a process that got underway this week.
Peretti told The Associated Press that members of the legal team have filed an intent to appeal the verdict but have yet to submit an appellate brief with supporting evidence.