From FANY website :
"The original uniform was a scarlet tunic with white facings, a navy blue riding skirt with three rows of white braid at the bottom and a hard topped scarlet hat with black leather peak. In 1912 the uniform was changed to a khaki tunic, khaki riding skirt and later a khaki soft cap."
They also show a recruiting photo of with the "original" uniform from 1908.
And a great full uniform photo from 1909:
"1909: Original uniform
FANY wearing the original uniform of circular black skirt and scarlet tunic with white frogging"
https://www.fany.org.uk/history/photographic-archive
I've no idea about the badges worn , I'll leave that to others.