It sounds more like teething than a reaction to the cow's milk, especially if it's limited to nighttime. Any change in her poop?
How is baby's solids intake? I guess you could try to give her a solids snack at 3 pm rather than the cow's milk. It does sound like she's getting plenty of dairy - I'm guessing what the pediatrician is getting at is that if baby is getting lots of cow's milk, which she might not need all of since you're still nursing quite a bit, that might hinder her transition to solids. On the other hand, not all babies are enthusiastic about solids at just a year. If that's the case you could try to give the solids first, then the cow's milk.