Call with QQ and no reads?

This might be a dumb question but I'll ask anyway.

I 3bet as UTG is a big fish who has called numerous 3bets OOP and I'm looking to build the pot with a good hand.

This is villains 3rd hand at the table. He folded his blinds in the previous 2. Mathematically I think it's a call but it is a 4bet to call with no reads so I'm unsure.

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) - PokerStars Converter Tool from FlopTurnRiver.com

CO ($8.78)
Button ($3.85)
SB ($10.40)
BB ($4)
UTG ($14.24)
Hero (MP) ($12.28)

Preflop: Hero is MP with Q, Q
UTG bets $0.30, Hero raises to $1, 1 fold, Button raises to $3.85 (All-In), 3 folds, Hero calls $2.85

Flop: ($8.15) A, 8, 5 (2 players, 1 all-in)

Turn: ($8.15) J (2 players, 1 all-in)

River: ($8.15) 4 (2 players, 1 all-in)

Total pot: $8.15 | Rake: $0.40

From pokerstove -
equity win tie pots won pots tied
Hand 0: 39.857% 39.64% 00.22% 19005028 104399.00 { QdQh }
Hand 1: 60.143% 59.92% 00.22% 28730686 104399.00 { KK+, AKs, AKo }

Is he really 4betting his 3rd hand at the table with AK though? At these stakes I think it is definitely a genuine possibility. However, take that out AKo and our equity drops to 27% and take out AKs and our equity drops to 18.2%

I believe we have 34.9% equity to call.

Anyone else making this call with no reads into a 4bet pot or should I learn to give up Queens in situations like this?