Are southpaws only lefthanded?

Chad Dawson is also right handed but fights as a southpaw

 

There aren't many more difficult things than fighting a tall southpaw. If you can develop a good jab, which you should be able to fairly easily with being right handed, you could be a stylistic nightmare for almost anyone. There will be weaknesses, especially the susceptibility to the right hand (from an orthodox fighter), but if you manage the distance well, this shouldn't be to much of a problem.

Run with it for a little while and see how you get on.