I am from the High Desert of Ca. (Lancaster). I can't imagine any plant that is goat-proof,they will chew anything.(Shoes,fences,etc,...) The trees will need wire all the way around them and farther up than the goats can reach "hopping" on thier back legs. My guess would be 10ft. There also needs to be a space of about 6"(kinda guessing here) betwwen the wire and the tree so the goats can't eat through the wire.Clever little buggers. A wire "bubble" around flowers might work. I'd just pen the goats and be done with it. I know someone with 10ft fountain grass that lets the goats out once in awhile. The stuff will leave cuts on human skin.The grass might be too big to make a difference with one goat?
Drought resistant plants can be poisonous. I'd stay away from Datura,Lantana and yellow Sage to name a few.PJ

Having owned a goat for about 6 years. The Boxwood shrubs that stood about six feet tall, gone. Cucumber could stand on her hind legs to over 6 feet tall (she didn't like my ex).
Oddly enough she didn't like cucumber, the veggies not the plant, if it was green she would eat it, we used her a asort of lawn mower for the 3+ acres of property. We would bring the dogs in for the day and let her wander around and eat the weeds, she liked mustard, and black eyed suzies. She never ate the pine, eucalyptus, or roses. But that might have been because she was very well fed on grass, mustard, alfalfa (regular feed) and the figs that dropped into her pen.

I don't think anything anything eats creosote (Larrea tridentata)...

"(what the heck are those "leaves" called anyway?!)"

If you mean on prickly pear or the like (i.e., these things), they're called cladophylls, or, more informally, pads or joints. I like the word cladophyll since it describes what the things are to some extent... "clade" means "branch", "phyll" means "leaf", and the pads are branches that perform the functions of leaves.

Patrick Alexander

How about Red Squill. Scilla is a summer dormant perennial bulb and is relatively drought
tolerant.

Ankrara's Hobby Corner

I think I've read that desert iguanas eat creosote leaves. As for goats, I couldn't say.

"I think I've read that desert iguanas eat creosote leaves."

The flowers I know they eat... I don't think they eat the leaves, though, and I've never heard of them doing damage to the plant. Desert iguanas also don't occur in anything I'd call "high desert"...

Patrick Alexander