The piece is "Maka Agha Khanam wife of Prince Rukh granting an interview to Tuku Khanam complete" - folio 72a, c of the Timur Nama - Akbar's commissioned work done by his studio of illuminators, chronicalling the life of his great-great-grandfather, Timur. It appears in the book "Imaging sound : an ethnomusicological study of music, art, and culture in Mughal India" by Bonnie C. Wade in 1998, and is apparently in the provenance of the Khuda Bakhsh Oriental Public Library in India. There's a copy at the Internet Archive, where you can borrow the book electronically. This image is on page 304 of the webdoc.
I have isolated 24 women in the miniature, to peer closer at their hats. There are several different types of hats here, along with other head coverings and a variety of clothes. While this does represent Babur's court, these images were painted a half century later, and I suspect the fashion of 1580 is of influence in the clothing worn.
Here are the images.
I may comment more on this later (I'm on deadline) but I was just so blown away by the variations in this single miniature, I had to post.
