at 4-5AM? We're doomed.
On the other hand, mid-night Kyoto is plenty safe for walking around.
I've flown with toddlers a few times and have always been amazed with how quickly they adjust. First, I think the travel just plain poops them out as they are getting on and off plains and eating at weird hours, etc., but the sun, the glorious sun really does regulate even toddlers really fast. They see it's dark, they see mom and dad sleeping, so they try too for as long as they can. Of course, I've only done Europe, but they adjusted within the first day. Japan? That might take a few, but it will happen!
Congrats on a hopefully successful flight. Good luck with the 10 hour time difference.
Japan as a whole is wonderfully safe to walk around - as a single young woman in '94, I was walking around Tokyo late at night with no problemos.
Our son is 16 months, we struggled with the time change to the US back in October. Although we don't co-sleep, in the end we just put him in bed between us at 4/5am and cuddled him, but didn't talk or interact with him. He fast got the idea that Mummy and Daddy were boring at that time of the morning, and went back to sleep until a more human(e) time.
Just this past weekend, Lifehacker blogged about a site called WeJustGotBack.com that's full of great stuff about traveling with kids. There is a tip sheet full of readers' advice on flying with kids (as well as one for road trips, visiting museums, and so on). Bon voyage. It'll be fine.