I had some scrap fur that was stretchy, simply stretched it over the sphere than sewed it in place.  Lucked out on that one :D 

But now I am curious, what do you mean by gather?

I would imagine he means something like this technique that is used to make a round nose for a puppet.

Had a friend do a quick sketch to give me something visual, and this is what he came up with after seeing the head:



Yup, Dino.  I could do a few things to take it back to a dragon, but I like it   Picked up some sew foam for egg, and gonna attempt to do a basic frame out of swimming noodles.  I am thinking bending them into circles with a hula hoop inserted, than cutting up some noodles and using 3 or 4 of them "per level" to hold the hoops upright.  The plan is to split the egg into 2, front and back, and connect them with velcro.  Not sure how it will work, but not an expensive attempt. 

He is going to be cute!  You'll have to let us know how the swimming noodles work out.  I am not real sure they well have the strength that is needed but they may.  If they don't then look for the plastic tubing at hardware stores used for water lines. Not the heavy PVC but the flexible stuff that comes in a roll or coil.