I can only share our anecdote - when we switched DS to whole milk his poop got really weird for about a week or two. It was pretty runny and sometimes even white colored. It didn't last long though and now he is just fine with regular milk. I mentioned it to the pedi when we went in for our regular 1 yr appt and he didn't seem concerned. It was a little strange to me though, because I think most of the stuff I googled mentioned constipation as a problem when switching to wcm, but we had the opposite.
My kids all have milk allergies and I nursed so I don't have direct experience. But, I feel like I have read several times about people having issues similar to what you describe and/or going the other way with constipation. From what I have read about dairy in general too is that it is rather hard on the body so it's possible she just needs some adjustment time.
How much has she been having? Can you introduce it slower and see if that helps?
Or maybe the milk in formula is more broken down so she could tolerate that but does have some intolerance to it so the straight milk is more upsetting? I'm not sure.