We went wehn DS1 was 7 mo. It was fine, but a challenge! I went to buy food for him in a supermarket, and hadn't got a clue....at least bananas looked the same!! He survived, as did we (would love to go back).
Also found everyone incredibly polite and helpful.
The transport network was difficult though - I am sure it is superb if you speak Japanese, but we weren't there long enough to "get" it!
Oh, and if your DD is still on formula, then yes, take it with you, but you can get cartons of cow's milk in every convenience store, and you rarely have to walk more than 5 minutes to find a convenience store in a Japanese city.
What's your budget? If you're looking to keep costs down, the Toyoko Inn group has a big chain of medium-sized no-frills hotels all over Japan, and they do family rooms, buffet breakfasts, have laundry facilities (very handy if travelling with a toddler) and so on.
But if it's likely to be a one-off trip to Japan, I'd really recommend staying at least a night or two in a traditional ryokan to get a taste of traditional Japanese-style living. There aren't many ryokan in Tokyo, but lots in Kyoto, and if you only have a week, then splitting it between Tokyo and Kyoto (new v old Japan) would make sense.
On our last trip to Japan last year (we used to live there and go back to visit most years) the DCs and I spent a couple of nights in this place - Yoshi-ima Ryokan - which is a traditional but foreigner-friendly ryokan right in the middle of Gion in Kyoto. We had a huge tatami room, divided into two, with private bathroom. One good thing about the Yoshi-Ima as far as I was concerned was that you can opt to just have bed and breakfast, rather than dinner being included in the room rate as at most ryokans - we're vegetarian, and most ryokans don't cater for that. It also worked out cheaper to eat out, and gave us more flexibility with timing, as ryokan dinners are usually quite early. But we did get a full Japanese breakfast served in our room, which was great.
The cost of return shinkansen tickets Tokyo-Kyoto is usually a bit more than a week's Japan Rail Pass, which makes it worth getting the pass as you can also use it on overground trains in Tokyo and some other short excursions (though bear in mind you can't use the rail pass on the very fastest, newest shinkansens to Kyoto).
I agree that everything in Japan seems very expensive these days - I remember when it was Y200 to £1, but now it's more like Y140. Hundred-yen shops are still good value, though (like pound shops but much, much better).
We went to Japan when DS was 22 months old (DD was 5). We flew in Osaka, visited Kyoto and then took the bullet train to Tokyo.
We stayed in a combination of hotels & serviced apartments (these were great because we could have breakfast in). Food wasn't a problem at all though DS did miss his milk as he was (and is still) a bit of a milk monster.
Found it really easy to travel around too. Just take a lightweight pushchair for carrying down the stairs to the subway.