Early stages of a $50 tournament, I have about 8.5k in chips, we are at 50/100 blinds.
Two early position limps, I make it 500 in MP with KQo. BB and both limpers call.
Flop comes Q84 w/2 clubs. Checks to me, I bet 800, BB calls, limpers fold. I put BB on either a worse Q, an 8, or a club draw.
Turn 4, BB checks, I bet 1800, BB snap calls. I now put her on a decent Q, or a strong club draw.
River offsuit A, she almost snap shoves for 3100. Bricked out nut flush draw gets there, but I dont think she shoves river with that. I'm thinking she may be trying to get me off a chopped pot. In the end, I decided I can't fold (3.1k to win a pot of over 10k) and decide to call. She turns over AQo. Im retrospect, clearly I was behind the entire time, but I could just not put her on that given the way the hand was played. The hand just put a weird taste in my mouth.
Did I get outplayed? Could I have done anything differently? Did she just take a very strange line and I simply just got coolered?
Thanks in advance for any thoughts.

Seems fine. She should have enough busted draws to make calling ok, esp. if you don't have the Kc.

I think you played fine until the river, when she lead snap shove like that seems to me the standard strong play from mostly weak players that are too afraid to lose value by checking so they do that.

Besides the odds, i feel like you can sometimes fold this spot bc i don't think people do that bet to push you out from a chop pot very often, and i'm pretty sure she can do that with an A so you can't check behind a Q.

Another thing is you didn't tell her image, if she was tight the chance she's bluffing is very low.

I agree this. The river shove more often is a strong hand not wanting to lose value from a check behind far more often than it is a bluff. The ace coming down is actually a better card for your range then hers yet dispite the ace shes allin? Sounds like alarm bells to me... I would only put her on a bluff if we had reads to justify doing so, otherwise from nits and the vast majority of players its a really strong line