Hi & welcome, ballcock = float valve & they are made of brass, so do not rust as such.
Main thing to find out before attempting anything is can you shut the water off to it ?? If so, then it might be worth a go, just make sure you have a replacement one handy most domestic ones are still 1/2" BS1010 brass & what is called a part 1 (i.e. water comes out straight down into the cistern) although you can replace like for like I would recommend you by a Part 2 (water comes out at the top & there is a little plastic spout to send it down).
If all goes well you should be able to just replace the working parts inside the cistern by undoing the union nut on the old & new ones & exchanging parts leaving pipe connection in place.
Hope the helps & make sense.