My Pediatrician wanted me to wean my daughter to only 12 oz. by the time she was 12 months. I am really surprised they would recommend cows milk before a year old, even with her being that close.
Are you giving juice or water or any other liquids? I just give my 18 month old daughter 9 oz. milk (now we use soy) in the am, and then water all day long. She eats lots of fruit, so my pedi didn't feel any need to give fruit juices as they are high in simple sugars.
Don't feel like you need to trick her into drinking her milk, it is a bad habit and might result in a picky eater. I'd recommend cutting out all liquids other than milk and water. When she's thirsty offer these options only. She might give you a hard time for a day or so, but she'll get thirsty and drink, and a day or so like that is not a risk for dehydration. The goal is 20 oz. of liquid a day. If she's filling up on other fluids, she's getting empty calories from those things and probably prefers the sweet taste to milk.
I wouldn't be concerned about nutrition if the things she's eating are whole grains, fruits, vegetables (unprocessed for both of those), and proteins. Keep the processed foods to a rare minimum and your baby will be healthy. Remember milk is a very calorie concentrated food. Obviously you don't have this problem, but my nephew (4 years old) only wants to drink milk, juice or soda all day long, and then won't eat normal food. I worry about the long term affects of this, as these are all high calorie, but low nutritional foods.
One other thing that my pedi warned me about. Don't freak out as they begin to slim down after the first year. They may even drop a diaper/pants size. This is okay and NORMAL. This is the time they burn the baby fat, keeping them chubby (eating more calories then they should) will put them at risk for weight battles the rest of their lives as they are learning to enjoy richer foods. Now is the time to train their taste buds so that they'll enjoy healthful foods!
Best wishes! :)