It is more than possible, but it would make much more sense to buy one. Better and cheaper, can't get better than that, all using off the shelf hardware.
10M is within the range of bluetooth even, not sure if it exists though, but there are definately wireless cams available! This is definitely something you do not want to build yourself!
You could get a raspberry pi or similar with WIFI, and hook the webcam up to that. It would probably cost around the same as a wireless webcam (they seem pricey for what they are) but then you would have the raspberry pi for future projects.