I don’t have puppy experience with the rabbit, but I do have puppy experience and bunny experience separately. When I introduced my dogs to the rabbit, it was very easy, as they were already adults and listened very well. Having the puppy and bunny getting used to each of their smells is great. The rabbit will be less likely to freak out about the weird smelling creature, and the puppy will have at least an idea that he is not the only furry in the house. 4 months old is a perfectly trainable age, so once the basic commands are followed everytime: sit, stay, come, down… and NO (haha), maybe add “leave it”, I think it would be a good time to begin face to face intros. I would do this on a leash, keeping full control of the pup at all times. Even if the pup isn’t aggressive towards the bun, puppies are full of energy and could hurt the bunny with a misdirected pounce, or even chase the bun wanting to play.
If you find the puppy is more laid back and not extremely energetic, it might be ok to let the rabbit and pup have free roam at the same time (with supervision). But I would still be sure there are safe zones for the bun to easily escape the pup, like hidey boxes with 2 exits, tubes, etc. From what I have observed thru videos online, and listening to other multiple pet households, many times the buns will be the ruler of the house. They can be quite intimidating! You would need to gauge the reaction of the pup, whether or not a lunge from the rabbit meant as a warning will excite the puppy into play-mode, or put him in his place (from the buns perspective).
I’m sure others here will be adding their experiences!! Good luck!! And Welcome to BB!