Yes. The answer is that you can do anything that any other 13 year old can do and that type 1 diabetes should never ever be a reason to stop you from doing what you want to do!!
You just need a bit more planning and to think things through a bit more than everyone else. I just got back from a few days camping, and here's a few tips.
The worst thing is hypos, so make sure you take plenty of stuff to treat a hypo (including nighttime hypos) and that its always easy to get to. You might be carrying heavy camping stuff around or setting up tents so a hypo might be likely due to extra exertion, dextros in pocket is a good idea.
The next worse thing is really high blood sugar! Make sure you have enough insulin with you, and think about all the other things you need and take spares (pen needles, spare insulin pen, spare tester, extra strips, batteries for meter, spare finger pricked and finger pricked needles, pump spares if on a pump etc.. ) keep it in a bag so it's all in one place & easy to get to and keep that bag safe.
Finally make sure you have some money for snacks when out, try to eat at the same times as if you were at home (or at least have a snack) and take a mobile phone (and charger) and text your mum to tell her that your okay and promise you'll call her if you need any help!
Other than that, go camping and have fun like the other 13 year olds, and in the future always do whatever your friends are doing, just make sure you do enough planning and take everything you need -
Never let type 1 stop you from doing anything!!
Good luck.