Japan is great - but personally I wouldn't want to go with a 9 month old.
I mean, you can.. and Japan is so convenient and easy/safe that it won't be a problem. But you certainly won't be getting as much out of the trip as you would be without a 9 month or (or with an older child). And the 9 month old will get basically nothing from it... (Also really check the time of year, I wouldn't want to be taking a baby there in either the summer or winter. Very cold and very hot, depending on where you go)
When I went to Japan, it was amazing, but it was a trip full of moving. Trains, hikes, visiting, changing cities etc. I'm not saying you have to, but its a small and very well connected country that works well for "traveller" style of trips, where you hop between hotels and cities. Rather than "stay in one place for a week or two" holidays.
Could you do all of that with a baby? again yes, but would it be a worse trip? I'd say so.. nappies, breast feeding, prams, naps etc. all while trying to visit places, on and off trains, different hotels etc.
Personally I would wait. Which is actually what I'm doing. My family and I live very close to Japan, so it is only a couple of hours flight for us, and I've told my son that I'll take him when he is old enough to actually enjoy it fully. Enjoy the travelling, Enjoy all the unique Japanese culture/food/entertainment etc. He is 5 now, and just at the point where I think he would get a lot from the trip, and that it would actually be really fun to do with him, because I know how excited he will be to see all the pokemon, video game characters, anime characters. He is fine eating ramen, sushi, and other Japanese food, good at travelling with us, fine walking around temples/castles etc.
So personally, if at all possible, I would save your Japan trip until your child is older, and do something much more easy this year, that is more suitable for a baby. You'll end up having a much better time in Japan if you do.