I thought the Race for Life was for cancer charity as well.
I think you might have difficulty raising money for this as a charity too as from the look of the site, you'd only be spending a few weeks actually doing any kind of voluntary work. If someone was going on a proper full time voluntary placement I'd be more willing to sponser them.
Have you looked around for jobs? I worked when I was under 16, you might not get much money for it but surely going off on an amazing adventure would feel so much sweeter if you have really worked for it.
I did all sorts when I was younger to get me through my studies, cleaning, working in all kinds of restaurants, cafes, a supermarket etc... I worked while at school and college and when I was at uni I wouldn't go home for the holidays, I'd stay and rent somewhere and work all sorts of hours. A strong work ethic is a valuable thing and it's a great feeling to think you've earnt something by working to pay for it.