1. Yes it will survive.

2. Give it a taller, more rigid fence.

ditto

3. Shoot the deer.

Deer eats foliage, you eat deer

Below is a pic of what I typically do. 4' high fence usually does the trick. I use either steel posts from Home Depot or oak stakes (mail order from companies that sell tree tubes). The painted steel stakes look better, if that is a consideration. Also deer netting rolls (cheap or heavier duty nylon both work). Cable ties sometimes come in handy to close it up. Footprint is maybe 5'x5' for wider growing trees like oaks. Once the oak is around 9 or 10' high, I remove the fence. May need to prune within the fence area to keep the real low branches from punching through the fence. Just an idea.

9 or 10 ft tall trees are perfect for bucks to scrap on with their antlers, thus killing the tree.