You can't join your FC on a different world but you can make a new character just for fun. I have a dozen alts or so myself just to play around with different aesthetics. It's what keeps me from using fantasias constantly and if a look really strikes me I will then fantasia my main.

.....I mean said alts are usually abandoned well before level 50, almost never make it out of ARR and are made exclusively on preferred servers to speed level... So....

but still!