The good think is the socialization window for a dog is between 6 and 14 weeks. I’m just taking a MOOC from the Royal vet school of Edinburgh, where I just read about this. This is a direct quote from a lecture, I hope I’m not breaking any copyright laws by giving it:

“Puppies have a socialization window from about six to 14 weeks of age. During this time, they will accept as normal any new experience that is introduced to them in a calm and positive manner. And this is the best time to build a positive associations with any potentially scary experiences.
 
For example, it’s really important that during this time, puppies are introduced to a variety of different people, especially children. And they should also experience traffic and other animals, too. Taking time to properly socialize your puppy can help to reduce the risk of developing behavior problems later in life.
 
It is also important to understand how dogs behave socially. The idea of an alpha dog is now very outdated. We now know that dogs do not have a linear dominance hierarchy as previously reported. Instead, they respond well to positive reinforcement training and consistency from their human handlers.” 

http://www.ed.ac.uk/studying/free-short-online-courses/subjects/medicine-vet/cats-and-dogs-mooc

With a really smart dog like a border collie, you should be able to fairly easy teach him/her what’s ok behavior around the buns and what’s not. I have a GSD and I never had a problem with her relationship with my buns, but she was 3 years when I got my first bun, so she wasn’t a puppy. We had also done a lot of obedience training. A GSD is very prone to listening to their humans, it’s way easier with dogs of breeds with a high will-to-please. Border collies are of that disposition too. 

Here is a thread that discusses the introduction of dog and rabbit. It has some very sound advice imo:

https://binkybunny.com/FORUM/tabid/54/aft/164067/Default.aspx#573141

I have a 9 month old border collie, who we got at about 9 weeks old. He’s a gorgeous dog, but he wont ever be allowed contact with the rabbits as it stands.

Border collies are crazy smart, but also insanely neurotic, once they fixate it is so hard to retrain them, and herding breeds are apparently a very bad idea with small animals (whoops!)

Despite multiple attempts at introduction and a lot of patience, and professional input at various stages, his ‘drive’ makes it impossible for it to work.
On the upside, it makes him amazingly gifted at things like fly ball and agility. (As the trainer we talked to phrased it “the better the working dog, the worse the pet” )

Despite doing everything by the book, our BC simply wasn’t suited to dealing with small animals safely.

We decided to stop interaction before the rabbits became an obsession (we had a sharp learning curve with the cat, with whom he is firmly obsessed) and we just keep them away from each other right now. There is a chance that as he matures he’ll calm down, but as he is now, he’s far too much energy for rabbits.

Im not trying to sound negative, but do be aware that even with doing everything properly there is a chance it wont work as planned-this type of interaction will be down to your rabbits and the type of border collie you have! So just to be aware that having a plan B might be a good idea!

My other dog is a border collie x springer spaniel, and she is an angel around the rabbits, although she met them when she was 5 years old, trained, and past the puppy exuberance by that point so it was a much easier introduction.

I really wish you the best with it!