This will be a long response, sorry:
Introducing any new animal takes time and space.
Sometimes the younger the better but older animals can work really well too. Most rescues and shelters can let you know if a dog has coexisted peacefully with cats/rabbits or other animals before adopting. Getting puppies is always a risk. On one hand they are young and you can mold them with training and socializing but you never know what their personalities are/will be like.
If you are set on a poodle do your research and talk to breeders or rescues. All reputable breeders should be able to tell you and show you the parents and know what their personalities are like. Breed rescues may also be able to give you info. But remember: Poodles are hunting dogs. They are water fowl dogs but not many people know that, so take that into account. They are very very smart but can be very excitable and energetic dogs. Any dog you get work with a trainer/and or a behaviorist to help you.
I have a lion head as well. He is my one and only rabbit and before him I knew nothing about rabbits. However I have worked with animals since I was 18. Specifically an animal caregiver at a no kill shelter so I am always around dogs and cats. My roommate brought Frodo home from work when his original owner abandoned him.
He came to live in an apartment with 3 older dogs in the spring/summer of 2012. One rat terrier (5 at the time), a hound/shepherd mix (1 1/2 at the time) and a pit bull (round 4 years at the time).
Let me preface this by saying that from the first moment this rabbit entered our house he had absolutely no fear of anything. He was not neutered at the time and honestly was very dominant and aggressive. (he is still very dominant but not as aggressive) But he has never shown any fear towards the dogs.
When it came to intros with the dogs my roommate and I went at Frodo’s pace. Knowing our dogs we were confidant that the only one that would give us any trouble was Lola the pitty. We were right.
We introduced Frodo to my rat terrier first. Parker was muzzled and leashed. Frodo had free reign of the room. Once Parker realized he could not chase/or bite the bunny he was fine. Within 3 days he could be in my room no muzzle or leash round Frodo. (My dog has always been afraid of Frodo, the biggest problem between those two was that Frodo would deliberately kick Parker out of his bed and I had to be very careful Frodo never hurt him because Parker would not stop the behavior).
Riley the 60 pound hound was introduced on leash as well. However she has no prey drive whatsoever so we never had to muzzle her. Frodo went right up to her and started climbing. Riley was leashed up every time they were introduced for about a week before she could be in my room with Frodo supervised with no problem.She still gets very confused because Frodo won’t play with her when she play bows to him.
Lola was the biggest issue. She has the highest prey drive of our 3 dogs. Frodo loves Lola, even though she wanted to eat him the first year plus we had him. She is an example of the time it can take to introduce animals. Until Frodo got his own room about a year after we got him, Lola could not be around frodo without a muzzle and/or leash. Anytime she got excited Frodo would be her first objection. When he got his own room she could see him move around and he could come up to her but she could not get to him which helped desensitize her. Before we moved in june 2014 Lola could be in Frodo’s room without leash or muzzle supervised with no problem. She tried often to play with him. Now he has a pen but not his own room. Riley and Parker are still perfectly fine with Frodo. Lola will never be trusted unsupervised but if she is calm and it is just her she can be out of her cage when Frodo is out.
We recently added an unexpected 4th dog (a 7 pound Chihuahua/terrier mix) to the pack. She is a brat. She is not allowed unsupervised with Frodo because she will go up and bite him. Than Frodo turns and looks at her and she runs screaming. It’s hilarious. Scooby will never be okay with Frodo unsupervised or really at all. She is alternately to confident in going after him but not scared enough to stop. She is the only dog that has ever bitten the rabbit. (let it be known she has never broken skin just gotten mouthfuls of fur because she can fit her muzzle through the cage bars) We put a stop to that quickly, Frodo had no qaulms about hurting scooby so we were careful.