to push or not to push

[gummy d]

First off i want to thank everyone hear for all the valuable information and laughs over the last year.i have been lurking regularly, finally signed up and am making my first post.
I'm in the small blind, everyone folds to me. I have about 20,000 in chips and am i'm tied with another guy for 3rd with respect to stacks. The big blind has about 35,000 in chips. Blinds are at 800/1600. I peek and find kk, raise to 3800 to go. Big blind raises 3000 more with what she thinks ( i believe she thinks) is the best hand. I raise all in which comes to 14,500 more after her re-raise. She thinks a bit, calls with qq (i put her on ak, aq, or a smaller pair [img]/images/graemlins/tongue.gif[/img]), flops a q and i'm done.
Question: Is there an argument for just calling her raise and taking it from there assuming i have a decent feel for when she does/ does not have a hand?
Generally when i'm out of position like this i prefer to go ahead and get it all in with the best hand even against a larger stack.
thanks in advance