In theory you could even book it the same day since its all UA. Maybe even at the ticket counter . The bigger question is what flights will have the XY booking code availability. These awards also do not have a minimum stay you could do a same day roundtrip. There is no expedite booking fee for 1K or UGS.

One thing I heard once, not sure if its true, that if you were booking a UA award on say US you are supposed to book it one day in advance.