JAL is switching over to a new reservation system so the format for domestic bookings is changing to a more standard six character one. I'm blanking on the timeline but it sounds like what you've got. The only reason I think you'd need to possibly
provide international flight information is if you book a Yokoso or Japan Explorer fare, regular domestic bookings shouldn't require it.

ETA: I've booked domestic flights through JAL's Japanese site and had no issues as a visitor. I'm not sure about the new system, but the old one would allow you to make a booking without payment and then it will cancel if you don't enter payment details within the timeframe (I think it was 48 hours or something like that for my particular fare). That's about the only thing I can think of to look out for.