I think that in the scenario you describe, the appropriate play, absent any reads, is to bet the flop and check the turn if it is checked around to you to take the free card.

If it is bet to you on the turn, you call if you are getting correct odds on your flush.

Consider two of your actions

1) you probably did not raise preflop
2) you bet after the flop

The lack of a preflop raise from late position (since you say it is checked around to you), probably indicates that you do not have pocket 8s or 9s. Perhaps you have pocket 4s. You may also have two pair 8s and 9s, but you are likely to have folded this hand preflop.

So chances are that your opponents will either put you on a pair or a flush draw.

So, now, when the Q comes on the board, they are likely to figure that, if your flush does not come in, you are likely beaten - unless you happen to hold JT - so in their minds, they only hands you are likely to have that are beating them at this point are 44 and JT - Q9 is a possibility too - but given that those are the ONLY 3 hands that are likely to be beating them at this moment, and given that your action thus far strongly indicates a flush draw, they are unlikely to fold their top pair or straight draws.