What are you using for your bearings between the rotating module and the frame?
Also, if this were to be made, how would you make the .125" sheet metal part? Getting that to line up nicely for a gearbox is easier said than done.
As others have said, the normal gears and their shafts can be held in place with snap rings or spacers. It is also useful to turn down the end of the 1/2" hex shaft to 1/2" round and use a round bearing to keep the shaft from sliding out. The bevel gears will have thrust loads, which are along the axis of the shaft so it's important to be aware of this in your design. Team 1640 uses a thrust bearing probably similar to this one
http://www.mcmaster.com/#6655k13/=smu6aw
I've also seen teams get away with using a thrust washer similar to this one
http://www.mcmaster.com/#5906k411/=smu6ry
Where do you plan on purchasing the bevel gears from? Also, where does the wheel go?