You should honestly go really slow with attempting to form a relationship with each other. Golden doodles tend to be hyper, as is any puppy, so your bun could get scared by the new addition. If your bun is free roam, you could put an x-pen up between the bun’s space and the pup’s space. It gives them a chance to get acquainted through the bars of the pen without your bun feeling stressed out by an interaction with something that could hurt it. If your bun isn’t free roam, I still suggest using an x-pen to let the bun exercise and still get interaction with the pup. Think about this from a bunny’s perspective. Buns are small, fragile creatures, predators. Puppy’s are larger, and are usually pretty excited at 8 weeks old. Like bonding bunnies, go slow with the process, and watch every interaction.

Hoping that your rabbit and dog become bffs is not a good idea.
It’s the same as hoping your cat and your bird become besties.

Can a dog and a bun live together peacefully? Yup 100%
Some can even get along well but this isnt something you can buy into, its really down to the animals personalities and is very rare.
Should you push them to be friends? No

Puppies are playful and rough and rabbits are easy to mistake for toys. Getting your puppy used to the smell of the rabbit is the first step. once it can smell the rabbit without getting excited then you can start the puppy seeing the rabbit, but it will need to learn it cant go near the rabbit, so putting it on the lead and letting the rabbit explore around the dog without letting the dog approach.
The most successful outcome is a dog that has no interest in the rabbit

Rabbits and dogs should never be trusted together without human supervision, if you want your rabbit to have a friend, look at getting him a rabbit companion

It can happen but only if you have full control over the puppy. Leave alone commands, or gentle, or say hi commands.

So time and patience will be required. In my experience, the bunny will be unaware of the danger, so you have to be 110% in control of dog.

Definitely get dog used to smell first and then he can approach when calm.

It would be good when approaching the breeder to say you have a bun and get them used to your bun’s smells as soon as puppies are born.. or very soon after. Their nose is first off the starting blocks when born, so that could be intelligent pre-preparation.

I agree with the others. You can always hope for the best, but if you go into this with the expectation that they will be friends, or even that they will be able to coexist peacefully without a barrier between them, I think you might be setting yourself up for disappointment. They’re prey and predator, nothing about their relationship will be easy, unfortunately. We just got a puppy a few months ago. He’s a GSP, so he will be similar in size to your pup. He is 7.5 months old now, weighing a bit over 40 lbs. There is no way in hell I would put him in a room with our rabbit, even if he was on a leash. He’s way too hyper, too big, too strong. One play bow at the wrong place, at the wrong time, and the bun’s spine would be crushed. We have two cats that he has been face to face with since we got him. He’s still having a hard time being calm around them. 30% of the time he’s fine, 70% of the time he goes bananas as soon as they show up and starts throwing puppy punches.  He spends a lot of time in the kitchen, which is adjacent to our bun’s room, they are separated by a baby gate. He can smell and see the bun, and he’s never gotten very excited about him. But I know that if the baby gate wasn’t there, he would lose it. I don’t expect to be able to let them meet face to face for a good while. First he has to get through the worst of his puppy craziness, and his obedience has to improve A LOT. It might take another year, maybe even two. Maybe I will never feel comfortable enough to try it, but that’s okay, as long as everyone stays safe.

Just take it slow, they might become friends, but sadly there are no guarantees.