Hey wanted to pop in and let you know my experience. DS was very poorly at 10 months (hospital 4 days) and it took a good while to get over it. He had been a massive eater from 6 months but stopped eating when he was ill and it seemed like the LONGEST time before he was back on solids properly even when he appeared to be fully well again.
I can remember being worried because he seemed to only accept dried fruit, of course I didn't want him to have too much of that fruit sugar and was also worried about him getting diarrhoea with too much dried fruit, but I was pleased that he would accept some sort of solids. Honestly during that time he took more milk than ever before and feeding him was almost like a new born again, even night feeds. I just kept offering small tastes of a variety of things that he had and had not had before and he gradually increased his diet again back to a good variety.
I think they know and trust milk, it's natural for them to take it if they feel slightly off or have had a bad experience with food or an illness.
Sorry I don't know how old your LO is but I wouldn't worry about how much milk/solids unless she is approaching 12 months. I personally wouldn't withhold milk feeds but would try solids JUST prior to milk, so if you usually do a milk at 11am for example try a solids snack at 10.45 and then the regular milk at 11am so there is a taste of something.