Bet and raise with no fear with no flush draw and a little straight draw on board. If you lose here, bad timing, nothing else.
Note: You were the lessor hand to begin with, the flop changed nothing. 44 is not a very good start, but usually is a winner when a set comes. Many times 44 should consider folding to a pre-flop raise. How did QQ play this? Who was the aggressor? If QQ was betting and raising, you could/should have folded before the flop. As always chip size, game type, player reads, etc come into play.
later,
