The 7-piece tablebase says that the position without the pawn on h6 is draw, so I believe this position is also a draw (by perpetual check).
A typical winning attempt in queen+pawn vs queen endgames is to find a position where white can block a check with his queen while at the same time giving check. This is not possible here since the black king is protected by pawns.
Another option is to hide behind the pawn somehow. A somewhat ideal situation would be if white could move the king to a8, and to have the white queen on the a-file (e.g. on a5). In this position there is no check on the a-file and if black checked on the 8th row, white could respond by queening the pawn. However even in this ideal position black has the single (but sufficient) resource of pinning the pawn along the h1-a8 diagonal.
So yes this position with the b-pawn is draw and you can almost freely arrange white king and queen and it still stays a draw.
If it was a c-pawn though it would be more difficult for black to hold this.