Are they worth going all in on in ring games?

Played a Q high diamond draw cheap on button. Flop two diamonds. Checked around to me and so I bet pot. One caller. Turn is a diamond. He bets minimum.

What would you do?

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Obviously, I went all in. He called and showed a A4d.

Should one even play Q high flush hands at all preflop? They are dominated by K and A high flushes and if I'm not willing to go All-in with an Q high flush then there's no reason to even play them preflop. I'm just wondering if the EV with Q high flushes is + with people's propensity of playing higher flushes vs lower flushes.