Ignoring the question of "what are you doing in the hand with Q6" for a moment...

The way I like to think of these situations is "what hands will he call a bet with?" This always depends upon your current situation, your table, the players, etc. In this situation with a handful of limpers, you might see hands like:
KT?
QJ?
66?

KQ PROBABLY would raise preflop. Again, depends on the player. K-rag is probably not something to worry about, certainly K6 is not a hand people usually play.

I would say that realistically the only hand you might be behind to in the situation you described is 66. There may also be something like a T9 on a draw, etc. Given that fact, I would simply just bet the flop pretty hard. Most of the time you're going to take it down there, as your 2-pair here is simply not a profitable hand in an unraised pot.