Snood is a good idea...
You can also band her mustache. I used to band Mimi's when she had full length hair.
Mimi side beard.jpg I used snag free bands but you can also use mini terry scrunchies.
This is a current pic of Mimi, she's kept in a shorter cut on the body & left longer on the legs. I cut her beard/ mustache shorter.
Mimi summer cut.jpg