I also just followed her lead - plus I was still breastfeeding and found out I was pregnant when she was 13 months, so my motivation to cut down on the milk was much higher!! You hear so many mixed things about what they "need" depending on who you listen to, but I think they don't "NEED" the milk after 12 months so I personally didn't force it if she didn't want it. Actually as soon as she turned 12 months, I did "don't offer don't refuse" so if she wanted it, she had to ask/indicate that was what she wanted - otherwise she got an alternative.
Some of my friends kids at the same age (15 months) are drinking a LOT of milk each day, some are drinking not as much. It seems like a lot of the ones who are big milk drinkers aren't as good with their solids, but maybe that's just coincidence? My daughter will eat nearly anything that we eat (tonight she was eating corn on the cob hehe) but isn't so good with the milk. She loves dairy though and asks for cheese multiple times through the day. And she drinks more water than me too!