We started gradually on cow's milk at 11 months with dd. We started by swapping the first bottle to a sippy cup with cows milk, and the rest of the bottles were still formula. The first day, she didn't drink any, because it was a new taste, and she'd only had water in the cup before. Every day, she drank more and more, until she was having a full cup. After a week or so, we swapped the second bottle, and worked up to the bottle before bed, which was the last one we swapped. We never gave her cows milk in a bottle, as we felt that this was a good way to stop bottles too. I think the last tub of formula ran out a few days after she turned one, from which time she was exclusively on cows milk.
I just wanted to add that dd had eczema since birth, but we'd never linked it to the formula. Her eczema got worse when she was solely on cows milk and we ended up on goats milk, which cleared the worst of it up. However, I don't think that starting one month early made any difference at all, as it would have happened anyway. She's fine now and drinks cows milk happily, although we can tell if she's been drinking a lot of milk at nursery, as the eczema flares up on her cheeks a little. We do plan to do the same process with ds though, as it worked well, both for transferring to milk, and getting rid of the bottles.