Well, same as anything else, I'd say check references. Does this person have other students? What do their parents think of the teaching? Would you be able to sit-in on a lesson and check them out.
Silly, but in keeping a teacher for the long haul, it would be good to sit with your daughter and talk about how this will fit into her life. What kind of committment is she willing to make? Then find a teacher that embodies that same 'play-ethic'.
~J