Eff stacks 100bb

Hero opens Qs Qd in CO 2.4x
57bb stack BTN calls
SB squeezes to 8bb
Hero elects to call
BTN calls

I elect to call here to keep the BTN, a presumed rec player due to his odd stack size, in the pot. In hindsight, that might be a better play (keep the fish in) when we're holding something less vulnerable than QQ. Perhaps I should reserve this line more for the KK and AA population of hands that are less overcard vulnerable.

As played, we see a Flop.

Flop (27bb): Qc Jd 9c

SB bets 12BB
Hero ???

I'm a little unsure the best thing to do here. Do we opt to Flat to try and keep the rec player in the pot? Or is the texture of this board so wet that we need to be ignoring the rec player in this situation? Ordinarily, if the board were say Q72r, I think this is an obvious flat.