Can't tell you anything about goat's milk, but I can tell you a little about weaning. I have an almost 13 month old, so we are just ahead of you. I am down to nursing just once a day (yeah!). This is my second child, so I am a little more relaxed about it this time around. Cow's milk is new, and most kids don't like it right away. Just keep offering it at mealtimes/snacktimes, and she'll get used to it. Don't worry if she doesn't take much, especially while she is still nursing a lot. My daughter didn't really start really drinking it until we started cutting out some of her feedings. The other thing is try to give her other forms of milk. YoBaby yogurt is great right now. It is made with whole milk. We open one up, pour a little bit of whole milk in, mix it up and put a straw in it. She sucks it right up. I have heard that YoBaby also makes a smoothie, but I haven't found it anywhere. When we are in a rush, we pop a straw through the foil of a Danimals (not whole milk, but her older sister's "wergert" of choice), and she sucks that up, too. This eased her transition to cow's milk.
Cheese counts, too, so push the cheese!
When you actually start weaning, you need to replace feedings with a snack. Fruit, yogurt, crackers, "big girl" food. Don't think that you just need to replace a nursing with a sippy of milk, any snack will do.