Hi babygiraffe,
You are in a good position in some ways as at 11.5 months milk is not so completely crucial as it is if your LO was a bit younger. The primary reason for giving milk from a year is for calcium, and there are a number of alternative sources besides milk. I was in a similar position to you at this age, planning to wean BF at a year (my choice) and I was very worried about getting her to drink milk from a cup. What I did was to gradually stop the BF one at a time (I think we did daytime, bedtime, morning) and just offer milk in a special cup at the time I would have BF. With the BT one I changed our routine from bath, BF, bed to BF, bath, stories, bed and then dropped the BF and offered milk in a cup instead.
For the first few weeks she actually took very little milk at each time, but I didn't force it and just made it available if she was interested. Often she had none at all. I made sure she also had access to water if she was thirsty, and gave her milk in other ways e.g. on cereal and in sauces. I also gave plenty of cheese and yoghurt so I could be sure she was getting calcium and fat in other ways. It was probably some time after I stopped bf altogether that suddenly she became far more interested in the milk from a cup and now she quite happily drinks a few oz in the morning and some before bedtime.
For us, the key was time and patience, and realising that even if she didn't take any at all that at this age that isn't such an issue and there are other ways to ensure that her nutritional needs are met.
I hope that helps a little