Hello fellow cake decorators, I am making this cake as we speak and I've run into a problem. I don't know how to make the plane stand. Help!!!

AInsert a skewer in the cake, pipe a bead of royal icing on the back of the plane and hold it against the skewer until it sets. Or melted white chocolate. Or a blob of wet gum paste or fondant.

Recently made a cake with a heavy gum paste mask.  I used a dowel (because of the size) and wet gum paste on the back and covered the dowel as well.  Didn't touch it for 24 hrs. until completely dry.  IMO a skewer would be fine for this plane.

Any one of the methods that AZCouture mentioned should work. I also noticed in your pic that the tail of the plane is resting on the cake - probably for stability. 

Attached is the mask pic - if you look towards the bottom you can see the dowel.