Hi kim. 4 months, how cute! *wag*
Does she do it with just you? Or everyone she spends time with? That might determine why she's doing it. Normally as she's so young that's just, as you said, excitable behaviour.
Well, our Collie is almost 3 now (they grow up so fast!) but initially he would nip in excitement. One thing that worked for us was, if he nipped during play (as that's one of the examples you've given), we would make it clear that his behaviour was unacceptable, giving him a loud "ah-ah", and immediately disengaging from the game, so he saw that his behaviour meant that the fun stopped! That's harder to do when you're out and about though, as you still have to continue the walk, even if it's only to take her home! Maybe someone else could provide better info on that.
Something else we found worked with Jack was yelping when he nipped, as it's a sound that I believe dogs can relate to and understand as an indicator of pain.
That's all a bit wordy, I hope it helps. It's usually only a phase, and as long as you are firm with her, it should subside.
Good luck :) Lisa x