I don't think there is such a thing as an "appropriate" age to wear a strapless dress. It all comes down to whether or not you feel comfortable wearing one, not whether other people think it is appropriate or not.
Besides, there's nothing to say that a strapless dress or top has to be especially grown up or "sexy". It could just be a cute look for summer when the weather is nice (and a perfect way to avoid strap lines).
The key with choosing the right clothes for the right time is to try not to wear something just because you think someone else will like it, or because it will make you look older. Chances are you'll feel uncomfortable in, or you'll feel as though it doesn't look quite right.
You'll always feel, and therefore probably look nicer if you wear something you love, that you're wearing for exactly that reason.
If you're a big fan of strapless tops and dresses, then I say go for it, and don't worry what anyone else might think! If not, then maybe wait a while until you feel more confident. Or you could wear a cardigan with it, so you feel less exposed?