There aren't any home pre season matches this time because of work being done on the pitch apparently and I've not heard anything about an open day, but that's not to say there definitely won't be one.
I don't know how feasible it is for you, but it seems that there is a Development team game being played at Treforest this afternoon, despite there being nothing on the Under 21 Twitter feed to confirm that - maybe you and your daughter could get to that?