As the owner of both goats and dogs, here are a few things for you to consider. The first is that housing different species together is generally a bad idea. Another is the need for animals, even those of the same species like dogs, to have their own space.
The last is the instinctual pattern of dog behavior where they chase things moving rapidly away from them. Again, a blanket statement, but as a breed designed to hunt, I'd be very hesitant to let a Cocker near livestock without specialized training or at the very least an evaluation.
If it were me, I'd wait for a sturdy pen for the goat first. Depending on your climate, the goat may need also need a shelter. Our pygmy goat uses a small doghouse, but the Nubian/Saanen cross at 200 pounds needed a shed. Young goats are amazingly agile so make sure it can't jump or climb out of the pen.
If the goat will have horns, check with your Vet. to see if they can safely be disbudded. Horns can cause serious injuries to pets as well as people. If the goat is a male, get it neutered fast before the hormones develop and it starts to stink. Intact male goats smell worse than skunks and it's a 24/7 stink. If you do not already know how to trim the hooves, take a good look at the baby's feet. That is what they should always look like.
Also, we had a very difficult time finding a Vet. that treats livestock. Ask someone with horses about that.
It is my opinion that dogs are unlikely to fight over the goat as if it were a toy. They would be more likely to injure the goat while trying to play. As the goat ages, unless you specifically train it to not do head butting, your dogs will become more likely to become injured.
