If I remember from the anime, Edolas controlled basically the entire world. So an army wouldn't be completely necessary except to quell rebellion, which is bound to not be uncommon in a kingdom that large. And I feel like it'd be hard to get a large enough voluntary army to keep order all over a landmass that size, especially with how they don't have modern medicine and thusly likely have a population of only 400-or-so million (Bassed off estimates of 1400), which is a lot, but I don't think you'd get a volunteer army large enough to maintain order all over the world like that. So the army would likely either be draft, or you get payed reasonably well for being in it

Edit:
[quote=@Zarkun]
And posted. Hope I didn't need to do James...
[/quote]

I missed this when you first said it, but yes, you needed to do James.