if you aren't sure if she got the dose, it's better to wait and see if her numbers rise rather than give her another dose. with a kid, it's much easier to treat a high than it is to treat lows - especially since she's in her honeymoon phase and has some of her own insulin. this way she won't have to be constantly eating because of double doses.
i never used pens, so i'm afraid i can't tell you if it's actually malfunctioning or not. if it appears she's actually getting the insulin, i wouldn't see a need to throw it away. have you tried drawing up the insulin and injecting it into the air to see if any insulin is coming out? that would be a way to tell if she's getting her doses or not. because it's only 1 unit, i wouldn't expect to see any insulin streaming through the air - probably more like a little bubble in the end of the needle or a little dribble. 1 unit of insulin is a tiny amount!