https://support.apple.com/en-us/HT211768
You kinda can, as long as someone in your household with an iPhone can set up the watch for your daughter as a family member. Someone has to have an iPhone in order to deal with setup and any access control and some features won’t be available without a companion iPhone, but it might be sufficient for your daughter’s needs. Then she can sign into the same iCloud account on the iPad. I can’t speak to how well it’ll behave between those two devices on the same iCloud account and how well anything like handoff or continuity will work because I haven’t had need to try it, but if you wanted her to have a watch and no phone I think this is the only way to do it right now.
I’ve never had the camera pull up from swiping right to left except from the Lock Screen, otherwise it just uses whatever app’s swipe controls are or from the Home Screen it goes into my second screen or App Library.
Same left to right, an active app uses its controls, the Home Screen or Lock Screen pulls up a widget drawer.
What app are you trying to use that has Apple’s Home Screen swipe commands overriding the app?