Trump was the first US president to make an official state visit to Qatar, and the stop culminated in a trade deal.
Syria's SDF is unlikely to follow the PKK's lead and disarm, but talks with Damascus could be bolstered.
White House says agreements signed by the US and Qatar would lead to an economic exchange worth at least $1.2 trillion.
The Georgetown scholar is among several US visa holders targeted for deportation for pro-Palestine advocacy.