The description of your daughter is pretty much exactly how I would have described my son.
He would always be on the move, doing laps of the living room and the garden, he always had to be running and he used to constantly climb on everything. If there was a chair, a table or a person nearby he had to climb on it. He also had no sense of danger or fear and he was draining! He also really loves cuddly toys.
He is a really picky eater, there are very limited things he will eat and trying to get him to try new foods would often lead to a mini melt down.
He also went through a phase of licking things and putting toys in his mouth.
Me and my husband were convinced that something just wasn’t ‘right’ but just couldn’t put our finger on it.
I spoke to his childminder endless times and she said she thought he was fine. She’s done extra training in Autism and all manner of conditions on the spectrum and she just kept reassuring us that she had no concerns about our son at all.
The good news is that he’s almost five now and most of the above behaviours have really calmed down or disappeared. The only residual behaviours are that he still has to climb on things (people included) and he still had periods of being really excitable. He can’t leave anything alone, he has to touch and play with most things he sees but I think he’s just creative and inquisitive.
I take comfort from the fact that his childminder isn’t concerned at all.
He starts school this September so I’m looking forward to seeing what his teacher makes of him and his excitability.
Its only over the last 6 months that I’ve started to see his quirky behaviours settle so try not to worry too much OP. Easier said than done though, I’ve been where you are.