Matt and Grace Huang were arrested shortly after their daughter, Gloria, died on January 15, said Alex Simpson, associate director of the nonprofit California Innocence Project. The Huangs adopted the child at age four from Ghana.
The couple's two other children, also adopted from Africa, have been banned from leaving the country and are being cared for by their grandmother, who is living with them there.
According to the California Innocence Project, the Huangs moved to Qatar in 2012 so Matt Huang could work as an engineer on two major infrastructure projects associated with improvements for the 2022 World Cup.
Their daughter would periodically refuse food for several days and then binge eat or get food from bizarre sources, such as garbage cans, a behaviour her parents traced to her impoverished upbringing, according to the website freemattandgrace.Com.
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When Gloria died, she was in one such episode and had not eaten in four days, leading Qatari officials to believe her parents starved her, Simpson said.
An investigative report also raised questions about why the Huangs would adopt children who did not share their "hereditary traits" and raised concerns that the children were part of a human trafficking operation or were "bought" for organ harvesting, according to the website.
"That's a fairly uncommon thing in any culture and that may have contributed to it and to the concern that something untoward and nefarious was going on," Simpson said.
The David House Agency, which is handling public relations for the case, did not immediately respond to a call or email seeking comment.