You will want a car. And while Disney's HHI resort is really nice - it isn't near the beach, and there are a lot of really nice places to rent around HHI for cheaper at that time of year. Disney's resort on HHI isn't overwhelmingly Disney, I've been multiple years during the period you are going and there aren't character meet and greets or anything. The pool has a slide and there is generally one or two (paid) craft activities for kids a day, which repeat a lot. Disney runs a shuttle to their beach house, but only their beach house - at HHI's own shuttle system is pretty sparse (if running at all) at that time of year.
HHI in February isn't swimming weather and when we are there, in our mid 50s, we feel YOUNG! Our young adult son joined us and was really young. The Disney resort will have some kids - some of the other resorts won't have anyone under 40 at that time of year. Its really a place of snowbirders (mostly for Ohio, for some reason, HHI is where Ohio snowbirds). There is little for kids to do on the island except the beach and pools - which in February (it looks like your DD is about nine).