BB 19/12/3b 6 over 300 hands

CO 38/16 over 40 hands

Prima, $0.05/$0.10 No Limit Hold'em Cash, 5 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $10.84 (108.4 bb)
BB: $10 (100 bb)
Hero (MP): $10.45 (104.5 bb)
CO: $9.85 (98.5 bb)
BTN: $15.40 (154 bb)

Preflop: Hero is MP with Q A
Hero raises to $0.30, CO calls $0.30, 2 folds, BB raises to $1.10, Hero ?

Always unsure what to do in these spots. The squeezer is really tight so I'm not sure I have a profitable flat here despite having a fishy player behind me who probably coldcalls and overcalls too wide. Since this is then one of the strongest hands with best blockers to a value 4betting range, I also thought about 4betting, but I'm not sure I wanna have a bluff 4betting range at all vs a player that tight. So is this just a fold then?