As others have said, it's been around for ages so it's really not a new thing that might end up going out of fashion anytime soon. I first joined the fandom in 2009 when I was about your age (13 or 14) and now I'm turning 20 in a month, so I've been in the fandom for about 6 years now and known about it for even longer and I have no intention whatsoever of leaving anytime soon.
I do know quite a few adult members as well, one of TFF's admins, WingedZephyr, for example is 26 I believe and I even know of a few members in their 30's and 40's. Though most older furs and 'Greymuzzles' are usually found at more different places.
Personally I would actually suggest you wait until you're a bit older before going to conventions and get a fursuit. For example, even if you did get a fursuit you'd probably end up growing out of it quite quickly (and ain't no one want a suit they're too big to wear in a year!)
Most conventions have age limitations, usually set as high 18 though some might be lower. This is because attendees of all ages will be there and things like alcohol is often available as well at the bar/restaurant and, simply put, the convention staff cannot be held responsible for that might happen to the minors attending the convention. It's not necessarily that conventions are an adult thing but rather that it's not really a 'child' thing either. If you'd somehow be allowed at a convention at your age of 13 you'd probably end up being the youngest one there, surrounded primarily by people in their early 20's (if not older).
