Sadly, you can't. Must level one, then get the reincarnation. I saw an option to trnasform a character into the new race but it ask to unlock the new race first (and exit their starting area), but don't really know how it works.
@Voltiga: i would like to know that too. There were players asking th same thing in-game.
What a shame. I don't htink i wanna invest time at leveling a new one. Had I been able to pick the new race I'd do it!
But meh.
Goo dluck all!