Next time post an interactive diagram so we can analyze on the spot
Offhand I'd play 1...Qb1 so if 2.Qd4 Qb3 forcing a trade of Queens
Eons (or millenium, I forget which) I read the entire chapter on Q+P endings in BCE and all I really got out of it was that you're better off being a pawn down with an active Queen than a pawn up with a passive Queen tied down to defending however many pawns you have.
FUN FACT: It is known that GM Geza Maroczy's specialty was Queen endings, a field in which he was almost unbeatable. The results of the following collection are quite eloquent: from all the Queen endings played, he lost only one…but because of time in a theoretical drawn position!
http://www.chessgames.com/perl/chesscollection?cid=1002796
for Black, to move. Black is moving up the board.
I couldnt find a plan, eventually lost the d pawn and offered a draw.