Should I have made a takeout double in the situation?
There's no one correct answer for a situation like this. It's a judgement call. I would have passed, for two reasons. One is that the club overcall means my CK is less likely to be useful. The other is that I was understrength for 1NT to begin with. The hand counts to 15 HCP, but it's worth somewhat less due to the lack of aces and the unprotected SQ. This evaluation method makes it 14.05:

http://www.jeff-goldsmith.org/cgi-bin/knr.cgi?hand=QT3+KQJ8+KJ93+K5

It looks as though no part score will make on this deal, do there doesn't seem to have been a lot at stake in your decision.