With how important family is to AJ, makes sense she'd want to continue it on and form one of her own.

It's one of the things I like about her. She seems to have everything figured out for her, wanting a simple, humble life taking care of all the important things in her life.

I kind of assumed that while Big Mac is the oldest, he's less interested in managing the farm than AJ, so she is the one that "owns" it.