Bad Call with AQ off?

this was i tourney that I completed over the weekend...Im +2 and the blinds are 500/1k...i have an effective stack of about 35k...i raise to about 3k...+3 (stack is about 30k) calls and dealer (stack is about 17k) calls. I have AhQd.

Flop is 10d 8h 6h

I check because im out of position, +3 checks, and the dealer instantaneous pushes all in (it was really fast).

so its 17k more to me with a pot of about 11k. I had a really strong tell from +3 that they were going to throw away there cards (novice player...practically handing her cards to the muck). So that wasn't what worried me. I put the girl/dealer on some sort of draw...probably a flush draw. And if that were the case, I knew she didn't have the nut flush draw and I still had two overs plus back door outs. I make the call and +3 folds. She shows 77.

Turn is a King and the River is a Jack.

Good play? Perhaps a c-bet out of position is proper here with a wet board like that?

missing info:

number of entrants
buyin
how many left
average stack sizes
reads on villain
your table image

in general:
make your raise size smaller
c-bet the flop

Keep in mind that when you have the Ah on this board you are blocking a huge portion of a reasonably tight player's flush draws so her range is going to be heavily weighted toward made hands.

you need to have a plan for the hand. You ended up calling it off with just overs after checking the flop, which surely broadens her range of bluffs/semibluffs but you probably don't have odds to call unless she's jamming a ton of brick hands like AJo. If you bet the flop then it becomes a pretty simple call.

Assuming she would shove with all overpairs and knowing no other information, I'd put her range at something like this:

Board: Td 8h 6h
Dead:

equity win tie pots won pots tied
Hand 0: 26.244% 25.66% 00.58% 14481 328.50 { AhQd }
Hand 1: 73.756% 73.17% 00.58% 41292 328.50 { TT-66, ATs, KhQh, KhJh, KTs, Kh9h, QhJh, QTs, Qh9h, J9s+, ATo, KTo }