We took our 13mth and 2.5 year old to Japan, and we all had a great time.
Not massively 'stroller friendly', so an Ergo carrier or similar is good. That said, we took a stroller and it was fine.
Public toilets were all very child friendly with changing tables and seats with harnesses to park little ones in while you had a wee.
Nappies, wipes etc were in pharmacies rather than supermarkets. Pharmacies were very common, so you didn't have to look. Not sure about baby food though. We took some pouches for emergencies, but our kids ate a lot of noodles etc. There were loads of Spar type stores which sold great snacks - boiled eggs, yoghurts etc. We did stop in a few Starbucks since they were reliable for sandwiches etc.
There were lots of playgrounds tucked away so it was nice to find a spot for a swing or slide.
We found a super play centre in a mall in Osaka which was full of babies and toddlers. But at 11 months, babies are happy with whatever! Crawling or toddling at temples etc sounds ideal.
We found Japan to be very child friendly. Everywhere was accommodating, lots of restaurants had kids menus/high chairs/cutlery/etc. Everyone was very friendly and very interested in our kids.
We flew with Emirates, and have done many times, with only good experiences.