I would call every time, and be favourite every time, like you were here!
The reason he pushes with a draw is because he thinks he's favourite, and wants to take down the pot whether he hits his draw or not. From his point of view he has 15 outs to make a flush or top pair with top/2nd kicker, or a flush (9 spades + 3 Queens + 3 Aces). 14+ outs makes him a favourite. More importantly, he can take down the pot right here, and not have to worry about getting the right odds
when you bet the Turn, people making straights, or the action drying up when the third Club comes.
In fact he doesn't have all the outs he thinks he does, because one of his cards is a Queen and you have two of them. If he had A♠K♠ he'd be a slight favourite over your Queens, but since he could have AT-AK, you're ahead of his range, so call. You are in fact 53% to win.