Take out double at first opportunity to double?
I'm assuming that the cards in the question are your cards, in the conventional ordering of Spades, Hearts, Diamonds, Clubs.

You certainly can make a takeout double at this stage - you have a shortage of your opponent's bid suit, and no major shortages elsewhere - but the question is, do you really want to?  With such an uninspiringly flat hand, only 11 HCP, and a partner who has already indicated that she doesn't have an opening hand, it seems unlikely you're going to be able to seriously compete in this auction, even in the best case scenario.  Supposing you force your opponent to bid here - do you really want to end up in 2C or 2D with a marginal fit and about 20 points between you?  (Not entirely a rhetorical question - maybe if you have 60 below the line, or your opponents have 70 below it, you do!)

If you're not worried about ending up in a miserable minor-suit partscore or, even more likely, giving your opponents a little more information about the lie of the cards than they previously had, then this doesn't seem an actively diabolical bid.  In general though I would adhere to the rule of thumb "third hand low, fourth hand high": given that your hand in the fourth seat is so unexciting I'd usually just keep quiet and hope for more interesting cards next time around.