Sounds like my hounds. One of our dogs has an arrangement with a deer who got hit by a car a couple years ago, she and her fawns can hang out under the dog's favorite oak tree, but any other deer gets chased off with much noise.

However, I can't say we've noticed any reduction in the deer fecundity here because they get chased around. They simply learned to tolerate the occasional chase as a cost of living in our valley, which is evidently not too burdensome on them.

Lol, you don't really need to selectively breed dogs to chase animals. All dogs have what's called a "prey drive," to an extent, which is essentially their inborn desire to hunt other animals. It's left over from when they were wolves. Different breeds have higher or lower prey drives, so it's not at all uniform from breed to breed or dog to dog.

I'm thinking breed them to chase them... I'm thinking in a manageable way.

Any dog will chase them, and then the dog will also run out into the road. We don't want dogs doing that ;)

You're talking about training, not breeding. Training is what makes a herding animal herd rather than run off in the woods and chase deer. :)

Valid point. Although I'll be picky and say that breeding plays into that .... but admit I don't want to bread a whole new dog for this imaginary and possibly unproductive job ;)

Breeding is a factor with pretty much anything when it comes to dogs. Hypothetically, you'd want a dog fast enough to at least sort of keep up with the deer, sturdy enough that Bambi isn't going to beat him up too badly if he gets too close, and smart enough to know that Bambi can be pretty mean if he has to be. This, of course, is on top of having enough of a prey drive to actually want to chase after Bambi, and trainable enough to learn how to do it so Bambi doesn't kick the crap out of him.

Putting all that into the Dog-O-Matic(TM) Computer....

... WORKING...

... beep boop Beep beep ker-chunk boop boop

... DING!

THE MOST SUITABLE DOG FOR YOUR REQUIREMENTS IS: the Scottish Deerhound[0].

====================

Of course, there are other dogs that would do just as well, like the Norwegian Elkhound[1], the Karelian Bear Dog[2,3], the Bluetick Coonhound[4, 5], or, even that well-known gentle giant, the Great Dane [6]. Believe it or not, Great Danes can run really, really fast. Their top speed is somewhere in the neighborhood of 30 mph[7]! Even Bambi might not be able to outrun that.

Whichever breed you choose, get your dog from a reputable breeder of working line dogs. Working dogs, show dogs, and pet dogs all tend to have different temperaments, and you'll have an easier time if you pick a dog from a line that's suited to his role. Frequently, the different lines will even have different physical characteristics[8, 9].

Not only that, but you'll want to make sure you pick a good breeder, and choose the dogs that will be most likely able to succeed at running down Bambi. For hunting dog breeds, at minimum, this means the dog's parents should have passed breed standard hunting trials, or the equivalent. The ultimate would be a pup whose parents are both field champions, or champions in some other doggie sport[11]. You want a star canine athlete, not a bench warmer.

Anyway...

TL;DR: Yes, breeding matters. No, you wouldn't have to create an entirely new dog breed to chase Bambi around. Pick a good breeder. Choose a dog based on his parents. You're looking for an athlete, not a pet.

---

[0]: https://www.akc.org/dog-breeds/scottish-deerhound/

[1]: https://www.akc.org/dog-breeds/norwegian-elkhound/

[2]: That sounds made up, doesn't it? Seriously, it sounds like something straight out of Star Trek.

[3]: https://www.akc.org/dog-breeds/karelian-bear-dog/

[4]: Watch out when talking about your Coonhound in polite company. These dogs live to chase and corner raccoons ("coons") up in trees, barking at them from the base of the tree while the hunter shoots at them.

Why be careful? Unfortunately, "coon" is an extremely offensive racial slur against Black people in the US. You really want to avoid that type of association with dogs, Black people, and trees, if you know what I mean.

See https://www.ferris.edu/jimcrow/coon/

[5]: https://www.akc.org/dog-breeds/bluetick-coonhound/

[6]: https://www.akc.org/dog-breeds/great-dane/

[7]: https://highlandcanine.com/the-fastest-dog-breeds-in-the-wor...

[8]: https://www.allshepherd.com/working-lines-german-shepherd-vs...

[9]: https://www.allshepherd.com/german-shepherd-sloping-back-vs-...

[10]: https://www.akcchf.org/canine-health/canine-athlete-performa...

[11]: https://en.wikipedia.org/wiki/Schutzhund

I think chasing them is a better, and easier, idea.