If you’ve got that much deer pressure and that large of an area, a dog is unlikely to help much. The deer will just keep an eye on where the dog is and come on over and eat and poop when the dog is at the far side of the property or asleep, or chasing another group of deer, then leave when they see him coming. Deer also can (and will, more often than people think) fight back. “Gored by buck” is not an uncommon history in vet hospitals in deer country, and even does will trample dogs if they think their fawn is threatened. An underground dog fence also isn’t appropriate for that setting. It’s ok (arguably) for letting a house dog out to piddle when somebody is home (and ideally out in the yard with the dog), but is very unlikely to reliably keep a dog contained 24/7 (particularly if they are the kind of dog that likes to chase things, as you theoretically want to go after the deer) and, as others have pointed out, won’t keep other critters out that can cause harm to the dog.
If I were in your place, I would pick an area to be a deer-free zone and fence it. Most reliable would be to use proper deer fencing (8 feet), but we don’t get any deer activity in our back yard with normal six-foot privacy fencing on two sides and five foot iron on one side. The deer have so many front yard, park, and green belt options that they don’t bother jumping the fences even though they easily could. I would not trust them not to come in if we were in drought and were still watering in the back, if I had a good crop of sweet corn going, etc. I will also say that we, and all of our abutting neighbors, have large to largish dogs that are episodically but not constantly out, which probably helps, as does the fact that our neighbor’s fences effectively act as a double fencing situation.