KK vs QQ flop -- did I play correct or just get lucky?

[crookdimwit]

Last week in a limit game I won a big hand, but in thinking about the hand afterwards, I'm wondering if I mis-played it, despite the big pot I won...

I'm in the small blind looking at K [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/club.gif[/img]. When the betting comes back to me, it's been raised by a middle-position player (Player 2). I re-raise. Button (Player 3) re-raises, which caps the betting. So there's me and two players left to see the flop.

FLOP: Q [img]/images/graemlins/diamond.gif[/img] Q [img]/images/graemlins/heart.gif[/img] 4 [img]/images/graemlins/club.gif[/img]

I bet, Player 2 raises. Player 3 re-raises. I cap it. Both players call.

Turn: K [img]/images/graemlins/spade.gif[/img]

Everyone comes out firing, and again, the round is capped.

River: 8 [img]/images/graemlins/heart.gif[/img]

I bet. Player 2 raises. Player 3 calls. I re-raise. Both players call.

I show my full-house. Player 2 shows AQ. Player 3 shows Q10. I take down the pot.

Looking back, though I realize I got lucky. With all the betting going on, I was worried someone had three queens. Not only was I right, but TWO players had be beat on the flop. On the turn, I hit my one-in-12 shot at getting one of the two remaining kings. But did I risk too much to get to that point? I doubt I would have called a re-raise after the turn, had anything but a king dropped, but by that point, I'd already invested a lot in the pot. On the other hand, most times, had I played the hand the same way, I suspect I would be in for a costly loss...

Did I play the hand correctly? Or did I mis-play it and get lucky?