Sounds like the rabbits need a better containment system otherwise, puppy (and cats) need more supervision. Give only restricted freedom when pup can't be watched.

Putting it into context with your dog's heritage might help!

Pyrs are flock guardians and with the right handling, they can grow to be gentle with all kinds of animals even if they make a few mistakes. Sometimes they are never trustworthy with farm poultry but often they are by the time they are 18 months to 2 years old.

On the farm, often all new animals need to be introduced to the pyr when brought in to the rest of the 'flock'. (Pyrs and other flock guards are known to separate new sheep or goats from the herd if they think the new guys don't belong - they like routine, changes in routine bother them and make them want to 'fix it'.... introductions to new stock are par for the course)

The best thing to do is to prevent mistakes -- by managing the environment to have few temptations. Use containment managment. Keep the small animals separate or keep the puppy in a separate area unless you are there with your eagle eyes while puppy is on a leash.

Leash time helps teach correct behavior... Plan to train. For example, spend time with the rabbits when you have the puppy on leash with you. Show the puppy how important the rabbits are to you. Comforting and low (not excited, not squeaky) voice tones. Let her see you handle the rabbits and show them to her, she can sniff, you can praise. Licking is off limits. Say no. Praise subdued behavior. If she's too wound up, then exercise her first. She should be relaxed, not be in an excited mood around your small animals when you do this training.

Otherwise, do not allow puppy to interact with small stock unless you are there. That comes later, in increments.

Set up for success. She should know you mostly for having soft voice and not for wanting to play or be hyper or do tuff war games. The soft gentleness teaches the same to her. Being rowdy with her and creating excitement should not take place during this initial training. As an adult, she might understand better but now is not the time to confuse her.
Consistency.

This is time when a shepherd in the Old World would be guiding the pup. Older dogs with the same flock would roll a bad puppy onto its back for doing something naughty like running through the herd. Shepherds would scold the puppy if the older dogs didn't get to the pup first.

Trainees go through a puppy stage of often being perfect and fooling you into trusting them, then they go, making a mistake. OR... in their adolescent stage sometimes taking complete leave of absence from their brains and all prior training! (adolescent stages in all breeds can be a challenge)

Mistakes. Try for zero defects. But accept that some mistakes can happen. Many farm dogs make mistakes before they are completely trustworthy with livestock and sometimes this period of time can last to 18 months or longer.

That's about farm animals. Sometimes a flock guardian does hurt one of its charges, could be a chicken or a lamb. Chewing off the ear of a cria (baby alpaca or llama). Chasing goats, whatever. These are behaviors to avoid teaching.

So the same rule goes... don't give any dog more freedom than has been earned. Some farm guardians I know have evicerated a baby lamb one time but then given more supervision, they become excellent with their stock.

Another note, on the farm, it is often a good rule not to raise the flock guard with animals that WILL teach the guardian to chase or hunt. It can make the work that much harder.