I would not introduce your dog to a bunny. A hunting dog especially, animals are unpredictable and you wouldn’t want anything to happen. That being said I don’t think you couldn’t get a bunny. You would just need to make sure that they will not be able to have access to each other and it would be best if they couldn’t see each other. Rabbit can go into shock if scared, there as been times were rabbits have seen a dog a go into shock although that is not common. Also if you do get a bunny it is best to have them in pairs, as they are very social animals.

Please see here for information on introducing dogs and rabbits: https://wabbitwiki.com/wiki/Relationships_with_rabbits#Dogs
It must be done with the utmost security measures, and if there is any indication that your dog will not interact well with your rabbit (or vice versa; rabbits can be the aggressor too), you must keep both animals separated at all times and securely done so.

Certain dogs will get along with certain rabbits. There needs to be both positive intentions and positive behavior (ex. A dog “playing” can be positive intentions, but the behavior is not positive for a rabbit). It is not unusual for a rabbit owner to need to permanently separate their rabbit from their dog/cat/other pet(s).

The breed of the dog doesn’t necessarily matter. What matters is personality and prey drive. You also need a bunny who has a strong, confident personality and isn’t terrified at the sight of a dog.

My first bunny Bandit was a dwarf hotot mix about 2lbs. Sometimes we needed to take care of my grandmother’s beagle Sassy, (definitely a hunting breed) for a week or two while she was away. Many times I’d catch Bandit and Sassy touching noses (maybe a greeting). The beagle would also sometimes be fast asleep on her side. On those occasions I’d see my rabbit, run a circle around her then he’d leap over the top of her like he was using her as a rabbit jump. He did it on many occasions.

Bandit also got along well with our two cats at that time. Now, 10+ years later our current netherland dwarf, Minyeong also gets along with our cat Nikko.

I think the fact that your dog did very well with your cat is a promising sign. Do you know how strong your dog’s drive is towards small mammals? Like does she react strongly to squirrels or wild rabbits? When she is fixated on something, does she respond to you? Does she know the “leave it” command? Typically the dog’s prey drive and training are the most important thing. And some dogs are really only driven to a certain type of prey and ignore all others.  @Hazel has a GSP who does great with her rabbits, but only with a lot of training and supervision. And they are always supervised closely.

I lived temporarily with my in-laws and they have a Germain Shorthaired Pointer who is generally very calm and well trained.  We tried doing a safe introduction to our cat and it was a NO WAY. The dog completely ignored us and just wanted to kill my cat (she was on a leash so it was all safe), but in her case her drive was just too strong and over-road her training, so we kept her in a separate part of the house.

There are members who just keep their rabbit and dog separate at all times, but this can be a very stressful situation for everyone. A few weeks ago a member had their husky break into their bedroom and almost kill their rabbit.

I think it’s great that you are considering all of these things and doing your research before hand. My first house bunny was actually a craigslist rescue from someone who had gotten a puppy and could no longer keep him.

I agree, it will depend on both animals. The dog needs to not have a strong prey drive and be able to follow commands even when something interests them. And the rabbit needs to be confident and not scared at the sight of a “predator”.