She's probably excited to be out and about and wants to explore her surroundings, which is completely normal. I find that taking snacks for my son to munch on and a couple of favoured small toys helps wonders.

Regarding the discipline, I don't think physical punishment is a good way to go about it. Even if you do decide to go that route, 15 months is way too young for smacking. What your daughter is doing may be frustrating, but it's what babies do.