May I ask why you have to get rid of your dog? While care for a dog is somewhat different than caring for goats, the 'farm chores' are work too. You may have to haul water to the goats if there is no facet near the goat area. You may need electricity for lighting or a heated water bucket in the winter if you have below freezing temperatures. Bedding needs to be changed, shelter needs to be clean. Depending on what you choose to use as bedding/ground covers, it can be everyday, week, month....for cleaning. The longer you wait, the more work it can be. You'll need to trim their hooves about every month...or hire someone to do it. Since you have to breed your doe to get milk after she gives birth, you have to decide what to do with the kids, keep or sell them? Disbud or let them grow horns? Depending on your does, you may be breeding at least one of them every year or so to keep milk steady coming. Of course, you don't have to breed any of them if you decide you don't want milk. Also, find out what sort of predators you have in your area and you'll need to protect them from them. A fox may not hurt your goat but your neighbor's big dog can. If you have coyote, mountain lion or bears, you'll need to think about locking them up every night even if you have electric fencing.
Goats are great. I love mine and it seems easier caring for them than caring for my dog. But I spent more time cleaning, feeding and making sure they have what they need than I spent on my dog. I can take my dog everywhere...even on vacation. You'll need to find someone to care for your goats. Goats are easy...dogs are too. That's why I ask why you get rid of your dog. Time spent on a dog may be different than spending on some goats, but pets are pets, they depend on you to care for them everyday...