how do you get a flat minnie mouse face to stand up on top layer of cake??

I would use flowed sugar. I used this technique in my Word World cake: http://cakecentral.com/gallery/2184394/matthews-birthday
and in the Lil Einstein's cake:
http://cakecentral.com/gallery/1475187/little-einsteins-birthday-cake

It is easy to do and with a backing of additional royal icing and a popsicle stick, relatively sturdy.
Hope this helps you,

Jan