You can do this!!!!! 1 yr olds shouldn't be getting much milk anyway. 16 oz max because we want them to be eating food, not drinking milk. You can try other milks besides cow too -- soy, rice, almond -- and see if she likes any of those any better. You can also add a drop of chocolate syrup to the milk to make it more palatable.
She will sleep SO much better without that night feed! You will be amazed. And you'll be surprised at how much happier she'll be during the day too, with solid night sleep under the belt. She probably seems happy right now, but toddler's esp. are more prone to meltdowns when they don't have that full night's sleep under their belt. And believe me, you don't want a sleep deprived 1 yr old!
It probably won't take as long as it did the first time, either. She's honestly probably just as ready as you are. Since she's older now as well, you might do something like put bandaids on your boobs and tell her mommy's boobs are broken. She's a bit young, but that actually might make sense to her.
Gooooooooooo Meltown!