An acquaintance of ours, who also lives in a rural area, had a possum come in through the cat door. Probably you wouldn't get coyotes coming to visit, but raccoons and possums and mice are a real possiblity. I wouldn't advise installing a pet door.
I'd take the dog for a long walk just before bedtime, and keep her in all night. A run would be nice, but definitely with a covering of some sort.

We have a critter door in our garage so the cats can get in from the weather in the winter. We are pretty rural and I would NOT put a critter door in our house. I currently do not have an animal that I want coming and going freely (very elderly dog who wanders, lots of ouside cats) so it isn't an issue. We have coons, possum, coyotes, and any number of wild animals running around here at night. I wouldn't think you have to worry about coyotes coming in but depending on your climate, coons and possum can get desperate for food and become quite bold when the weather turns cold and resources are scarce. I agree with Marlingardener, walk her or let her out before bed. I personally don't think it is safe for a small dog outside in a rural place overnight or unattended for an extended time. Lori

A coyote will jump a fence to get a cat or small dog - so put a roof on the run.

Coons and 'possums will learn to use a pet door and they can do a lot of damage inside your house (well, actually, you do the damage trying to convince them to leave!).

Thank you all. Seramas, I am so glad you mentioned that. I had heard of that once before but forgot. It is brilliant and I will pursue it.
That and a roof on our dog run. :)
Appreciate everyone taking the time to help.

My neighbors had a dog door with one of those electronic latches.

My cat learned to wait until the dog was close enough, then dash through the door and eat the dogfood.

LoL, lazygardens! Critters learn to adapt, pretty smart aren't they? Lori