Play multi-player on a friend's farm but with my character

So I looked up the FAQ but I didn't get my answer.

I've been playing this game for about a month (real life haha) and a friend suddenly started playing. I want to help her so we did everything to make multi-player work. However when she invited me (online), I thought it would carry over the character of my game to her farm - instead the game asked me to create a new character. Why is that? Can't I use mine on her game?