Restore iPhone from iCloud, without backup

Hi, I recently broke my iPhone after dropping it (the screen has broke, but the phone still seems to work, because there is a light that comes on) the battery went, so I cannot turn it on properly and connect it to my Mac to do an iTunes back up. When I log into the iCloud website all of my photos and everything is in my iCloud. Is there anyway I can make a back up from that? if I select back up from iCloud it says there is not back ups available.

Could I just start my new phone as a new device until I get the broken one repaired and then do the back up of the old phone later?

Thanks!