My son has ADHD and while being different from your daughter doesn't mean she can't have ADHD as well... our experience WAS different than what you're describing.
First, it wasn't a phase. There was no point at which my son STARTED to be hyperactive... he was super active from the beginning.
Second, his behavior was never about not LISTENING. He had/has very low impulse control so often even knowing not to do something couldn't stop him from doing it in that instant... BUT fixes like "hold my hand" worked really well.
Third, it was the same at preschool, at home, at play. Maybe most at school actually because he often got overstimulated by everything happening with other kids.
The big things we DID see in him were:
-An inability to be still (really from the time he was a baby). He was in constant motion. He could not sit still through a meal, a tv show, a conversation, a game, nothing. And he would move without knowing he was moving.
-He broke everything. Toys were always being broken or lost. It would devastate him that he had ruined it, but he'd break the next thing the next moment. Pages were constantly ripping in books (pop up books were the worst because he'd just open them too far), arms dislocated from dolls, building sticks breaking.
-He was/is EXTREMELY bright and noticed EVERYTHING, like there was no filter for important vs unimportant information. He would read every street sign, license plate, and menu, and interrupt conversations from across the room, or wander away from his own toys to pick up something that dropped on the other side of a playground.
To me, it sounds like your daughter is just being 4 years old and testing boundaries. If you think it's something more... or even if you don't... you can talk to her doctor. We forget that pediatricians often have helpful information about all aspects of child development, not just the medical stuff.
HTH
T.
