I've been thinking about this too. If we assume they 4-bet with TT+ then we only have a v.slight edge on equity:
Equity Win Tie Loss Hand
Player 1: 50.010 % 44.082 % 11.856 % 44.062 % QQ
Player 2: 49.990 % 44.062 % 11.856 % 44.082 % TT+
If we restrict the range further to JJ+:
Equity Win Tie Loss Hand
Player 1: 41.099 % 33.674 % 14.850 % 51.475 % QQ
Player 2: 58.901 % 51.475 % 14.850 % 33.674 % JJ+
And (and this for rush poker I think is the most reliable range) QQ+:
Equity Win Tie Loss Hand
Player 1: 41.099 % 33.674 % 14.850 % 51.475 % QQ
Player 2: 58.901 % 51.475 % 14.850 % 33.674 % JJ+
I only play Nl10 so this could be different to the limits you play - but I think a ok rule of thumb is unless we are against a shorter stack I just play QQ on implieds.