First, it's awesome that you're riding! Keept it up. Second, it's awesome that your grandson wants to ride a moped. Keep encouraging him!
Ok, I also agree that having a child on a bike seat in a moped may not be entirely safe. Granted. But kids do ride on motorcycles, which go much faster. I'd say that the best thing is to wait until your grandson is about five and a bit more alert to these kinds of things. But, if you ride really slow w/o traffic, I don't see a problem w/ him riding in a carrier seat. After all, bicycle riders do it all the time.
The best thing, however, may be to get either a top tank and/or a two-seater moped (if you don't have one already). When a bit older, your grandson can just sit behind and hang on (still, w/ a helmet). W/ a top tank, he can ride the tank. I used to ride like this on my dad and uncles' motorcycles from about that age (5-6) until I was too big, then I sat in the back.
Another suggestion ... is to build a side car. Now that would be a great idea, not just for carrying kids, but for transporting dogs. A Moped Army member in Kzoo was thinking about something like this for her dog, Taxi. A side car would probably be much safer and would be very hip, too.
Still another suggestion ... you could put your grandson in a child carrier backpack (I'm not sure what they're called). I'm sure you've seen them around. My parents used to have one in which they carried my little sister. They're mainly used for infants, but I think many toddlers would fit in them as well. I'm not sure if they're designed for riding on a bike or not ... but it's just another suggestion.
Finally, it's great that your grandson is interested in mopeds. It's a delicate balance, I'm sure, between indulging his interests, looking out for his safety, teaching him respect for the moped, but preventing him from developing a phobia of the machine. I'm sure you'll do the right thing. And I hope he grows up to ride mopeds! ;-)