9.5 months is still pretty young in my opinion. I would work on offering the sippy with just water in it and hold off on the milk for now. I know there are some people who give milk before a year but our pedi doesn't want us to offer it at all before a year. You still have 2.5 months before she's one....maybe push the milk back to 11 months and see if she's more ready at that point. I don't know that you need 2.5 months to slowly wean and I, personally, would be concerned that if I started the weaning process and it went faster than I was planning that then I would need to give formula until she was 1. (Nothing in the world wrong with giving formula, but my thinking is that I would prefer to just transition from breastmilk to cows milk rather than breastmilk to formula to cows milk. I less transition that way.)
If you are set at weaning at a year, then I wouldn't replace the night feeding with a bottle. If you are open to not completely weaning at a year, then keep that before bed feeding for a bit longer. She may surprise you and give it up on her own with no fight or stress on your part.
Good luck...just try not to stress and remember that she will take a cup and one day, this will all be a tiny blip on the radar when you look back.