You should have supplies if you need to evacuate, for the dog, rabbit and yourself.
For the rabbit, have a hard sided carrier with a blanket and food/water containers. Also have food, hay, and water to last a few days. A pen, pet tent or something similar is good to let her out of the carrier but still be safe. If she is litter trained, have a small box and some litter as well as a few cleaning supplies like a garbage bag and litter scoop. Keep medical records and other important papers in a known spot so you can grab them quickly. A small first aid kit can also be useful.
For the dog, you basically want the same stuff. Food, water, bowls, collar and leash and important documents. A crate or kennel is also goo to keep him safe and contained. An updated picture of you and the dog is helpful to prove ownership. ID on the collar is a must and a microchip is helpful.
For you, bring some basic food and water. Some dishes might also be useful. Also have some blankets, a radio, flashlight and other supplies.
I am not sure what the procedure for a tornado is. If you just have to go into your basement, then have stuff down there for the pets as well as some emergency supplies. If you need to evacuate, have the supplies ready so you just need to load the animals and get everything in the car.
It is a good idea to train you dog to at least be able to be around the rabbit. They don't have to get along and you don't have to let them out together, but the dog should be able to not harass the rabbit. Even in a best case seniaro, they would still have to be in a small area together. It might be a room in your house, the car or a hotel room. In these areas, it is hard to separate them all the time. If it did end up being more than a few hours, you could let one out to run around while the other is in a carrier or another room.
