What hands does he have that you beat? Let's see... Horrendously played AA/KK/JJ/TT, AQ, Q4, 94, maybe JT, and that's about it. Hands that beat you: QQ, 99, 44. There are a whole lot more ways to make the hands you beat than the ones that beat you (one way to make 99, one way to make QQ, 3 ways to make 44). I think you can severely downweight hands like Q4 and 94, plus TT-JJ... they just don't seem at all likely given the flop betting (even a loose player is mucking Q4 and 94, and prob raising TT-JJ).
Looking at his flop betting, when he puts that four bet in you're really looking at AA, KK, AQ, QQ, 99, and 44. That's it. AQ seems exxxxxtremely unlikely. You're getting 247: 127 to call, or basically 2:1. 12 ways to make AA & KK, 5 ways to make the others. You still have four outs twice against 44, which helps somewhat (whereas any hand that is behind you has fewer outs). Call and pray.
http://twodimes.net/h/?z=1593840
pokenum -h qc 9c - ah ad -- qs 9h 4c
Holdem Hi: 990 enumerated boards containing Qs 4c 9h
cards win %win lose %lose tie %tie EV
Qc 9c 747 75.45 243 24.55 0 0.00 0.755
Ad Ah 243 24.55 747 75.45 0 0.00 0.245