While it's lovely to see someone actually do some planning for a change (long story - another time), I think you need to consider the possibility that at each step in the process, your next step may be determined by the reaction you get (especially from the m-i-l to be).

Propose, certainly, first. Then see what your fiancée's thoughts are on how to proceed. If the reaction in Japan when you go over to meet the mother is something other than what you expect (and potential m-i-ls have a real track record of surprising the heck out you!) you may want to reconsider what step is the next to take. Or even whether or not to subject your parents to making a trip over to Japan.
Cheers,
Bev