The color of stool of kids will vary depending on the food ingested.
How ever, blood in stools is not normal.
Since you say it all started after starting Dairy milk, you have to get cow`s milk allergy
And she has completed 1 year. Hope she is on solid foods too. By 1 year of age, a kid must be able to eat what ever is made at home.
If not please start semisolid and solid foods soon.
Hope my answer helps you.