I had to finally just put my foot down with ds.
He is still a poor solids eater, but it's getting very gradually better. I look forward to future growth spurts when he can learn to eat other foods.
Anyway, my ds was exactly the same way. He's been that way always. At a year old you don't worry about it too much. But by 18 months old I knew he should be eating more solids and less milk. Too much milk actually causes intestinal bleeding and can cause anemia because the milk somehow interferes with iron absorbtion. So knowing this made me even more concerned about ds's lack of eating habits.
One major reason they like the milk is that it's easy. Two minutes of swallowing and the hunger is gone! Milk is choc full of nutrients so that helps keep his brain craving it. But you're the mommy and you know that she needs to learn to eat herself full and top it off with drink. Here's some of what I can remember of my journey toward normal eating for my son.
I just decided one day. Ok, really I decided one day that something needed to be done but chickened out of doing anything for probably a week. Then I tried to cut out milk to 8oz a day or something crazy like that and found out that that was too drastic of a change in one day. So then I decided on something more reasonable. But the point is that I started down the road. I didn't just worry anymore I took measures to correct the problem. I had to change my tactics, but you can't change something you've never started on.
I decided to allow 1/2 a cup of milk during lunch so that his belly would be full enough for a nap even if he consumed no solids during lunch - which happened quite a few times for the first month or so. I decided also to allow two cups of milk, one hour apart, after dinner, so that his belly would be sufficiently full for bedtime. I did this because I realized that my quest to get him eating solid foods was wrecking his ability to sleep and that just caused more problems. (Also, mixing medication with milk is still the only way I can reliably get him to take it and he was on medication at this time that he needed before nap and bed.)
I established a routine with the eating. We get up and eat breakfast in the same boring steps every day. Lunch is served in the same dish every day. All meals are at the same hour of the day. Snacks are consistent. This has really helped in the long run. Once all the other areas got ironed out in his mind, my consistency in this area helped bring him the extra mile with his eating.
I lowered my expectations about eating solid food. I accepted a measly teaspoon of food as his having eaten a meal. I found that I had to do this at first. This gave me insight about portion amounts:
https://babywhispererforums.com/index.php?topic=24957.0At first I had to give him one food at a time, allow him to eat as much as he wanted, and then clear that off and offer another food. But after offering the three or four foods that made up his dinner that was it. Whatever he ate or didn't eat was up to him. Now that we are several months down the road I can offer all four foods at one time and he can choose which to eat or not eat.
I did not cower and give him candy or junk just to be able to say he had eaten something.
I did not plead with him to eat, promise him treats for eating, promise the milk for eating a certain amount of food, or in any other way put pressure on him or make a battle out of the solid food. I think this is the key for a picky solids eater. Remember, they won't let themselves starve and this is an age when many children eat almost nothing all day long.
Your daughter is perfectly capable of understanding you if you tell her 'no milk' or tell her 'no milk until xx time' or even 'no milk until you eat (if you want to even try to fight that battle

I wouldn't, personally). My complication with my son is his speech delay. The child still can't even say 'milk'. You'll be able to go farther faster because of your daughter's language ability.
You will get tantrums. She will be upset. The rules have changed. Something she used to be in control of has been taken from her and she won't like that. That's why you have to be firm and resolute in your decisons. The first day was horrendous. I think he must have had 30 tantrums over not getting the milk when he wanted it. That was really hard for me to deal with. Then, he seemed to accept the new rules for a bit but then tantrumed all over about it later on. But I stayed consistent and by the end of a week he acted like the rules had always been they way they were.
Progress has been slow but steady. It was one step forward and two steps back for a time. That's frustrating. But I've stuck with trying to reach my goal and have made adjustments to my plan along the way. This has worked to get me where I am now.
That's all I have time for now. Ask me anything else if you want. Good luck to you!