Of course you can do permaculture without domestic animals. It just means that you'll do the work instead.
If you walk around a mostly undisturbed, healthy forest you don't see many animals walking around
If you're in and about a forest the mostly likely animal that you will see is a carnivore - and you're on the menu. I've live in a forested setting for years. And currently my property line goes into 'forest'. While deer are common at my current address, I'm still more likely to see sign of deer (footprints up to the side of the house, used for scratching) than the deer themselves. Just because you didn't see them, doesn't mean they're not there.