Matthew Huang was working in the booming Gulf nation as part of infrastructure improvements for Qatar's hosting of the 2022 World Cup.
The Huangs say their daughter, who was born in Ghana, died of medical problems complicated by unusual eating habits that included periods of binging and self-starvation.
They have two other African-born adopted children, who left Qatar in October to live with relatives in the U.S.
Qatar is a small Gulf nation whose local population is dwarfed by large numbers of foreign guest workers contributing to the breakneck development of the energy-rich nation.
The case raises questions about possible cultural misunderstandings in a conservative country where Western-style adoptions and cross-cultural families are relatively rare.
Prosecutors allege the couple denied food to Gloria and say she was locked in her room at night. A police investigation questioned why the couple would adopt children who don't share their "hereditary traits," according to the family's website.
Defense witnesses have testified that the girl appeared healthy and active just days before her death in January.