Ok, will have a look, but before I comment on the hand two things:
1) I posted this thing which is probably relevant to the direction the question goes: http://www.flopturnriver.com/phpBB2/...ts-t74733.html
2) Since your opponent isn't all-in with your quads it could be argued that you're not extracting maximum value. But as seen in point 1, maybe asking if you extract max value is the wrong question to ask?

Preflop I think is ok. If you were to raise it you would have to start considering commitment and a low pair isn't good enough for that. You can fit or fold here easily.
For the flop I like a lead out. Any queen will come along and if noone has a queen you won't be paid anyway. As played I also like a check-raise with similar argument. You're looking for a betting sequence that will get all the chips in the middle.
Turn check/raise is the right idea, but the min-raise is counterproductive imo. The effective stack behind is t1285 and if you want the rest to go in on the river (and you do) you'd like the stack behind to be about t800 or so with a stack above t1000 to make the all-in more callable. This suggests a raise to t450 which is almost as callable as the raise to t300. This would make the river pot t1230 with t835 behind - here you then push all-in and get called.
As played the river bet is just too small. Even as played you can shove the river - there's only t985 behind which is only a slight overbet. I think you were trying to partly get value from your bet and in part hoping he'd raise you all-in. If so, you're overthinking it. Play it more straightforward imo.

Look at it this way - on the river if you bet t985 he will fold 50% of the time and call 50% of the time. If you bet t300 he'll call 100% of the time and never raise. The chips already in the pot are yours either way. Your gain from shoving is average t492.5. Your gain from a t300 bet is t300. It's more profitable to shove (assuming my assumptions are near true).

If you want to make it complicated for yourself you can start saying that sometimes he shoves all-in if you weak bet, and the two counters are that sometimes he folds - and his shoving is probably less likely than you HOPE. Your estimates need to be realistic. At this time he's SCARED of what you have and happy to see a cheap showdown, no? Especially if he has a naked queen like QT. The bigger bets on earlier streets can make it so he'll have to call the river shove even if he thinks he might be behind.