I think there's a distinction between carrying a handgun for your own self defense and the notion of militia service for protection of the state. The OP actually doesn't say, but I was under the impression of the former.
However, as to the latter, I'm not really sure if compulsory militia service would work under the Constitution - it seems like another form of involuntary servitude, but I really need to think about it some more. Practically, I think it would be incredibly wise for each of the states to run a voluntary militia training program. No enrollment for basic training and such, just open up the training facilities and sessions to people of the local area (local area being key, just a simple DL check is all that's needed).
A little off topic, but I recently was thinking about joining a gym, but prices are rather high in my area. There's a NG station in our town so I got the idea that, if there's daily PT going on at the station, why couldn't local people join them each morning for a work out? It would help the community, help the NG recruitment, allow the community to see what happens there, etc. I couldn't think of a good reason NOT to allow this as long as civilian participants could drop out of the PT at any time.
I think that would be a great model for the 'unorganized militia'. If the local NG base does range training at 3pm on Thursdays, let the civilians join in with their own firearms. Who knows, their recruitment numbers may go up.
Same could be done for local police departments too.