Just for the sake of putting in an answer to get the ball rolling, Tom has already pointed to the best answer in the first comment: It would generally be somewhat difficult to get a seat at such a place, and the secret is if anything
the hotel you're staying at.
If you're at say the Four Seasons (the downtown one - not the Palace one! :) ) that is your best bet to get in to a basically very expensive joint like that.
The issue of your kid coming along is a difficult one. It's a complex and subtle issue.
1) on the face of it, as you go up the skill and fame level of chefs. you go through a pretentious region of the graph, BUT then at the extremely high end, they aren't pretentious at all. the guy might welcome, a kid eating there, with boisterous open arms.
2) remember that overwhelmingly Japan is just plain ridiculously, almost whackily, polite! (i.e., other than when they're not vomiting-everywhere-drunk). if you think about it - is there any country you could have asked about, that is less suitable to "take a chance" on being rude or ruining someone's evening - heh! In a sense, that's your answer there.
3) as a commenter explains, simply every kid is different. some are natural gourmands, grew up going to fancy restaurants in Paris where they were treated like family and it would be a total non-issue going to some overpriced sushi bar that's been on TV a few times. Others will act up, and totally ruin the night at $1000 a head for the other patrons.
(Note however that the same very much applies to some adults, heh!)
In summary, I'd say in answer to your question (1) how to get in to a staggeringly expensive, overly-famous restaurant - the specific answer is "you'll be staying at one of the top 1 or 2 hotels and it will be entirely up to them". Regarding your question (2) "Should I take a child along to a fancy-ass restaurant" there's no real answer. Note that even if someone here specifically replies "Oh sure, we take Darlene along all the time - Jiro loves her! She gets to sit on the bar!!" the answer just totally depends on the specific person involved.
BTW, unrelatedly I would recommend you consider instead going to Jiro's son's restaurant. (I mean, this is in no connection to your question about your child and so on - I'm just saying, I recommend forgetting about Jiro and going to his son's restaurant!)
BTW it goes without saying you have seen the documentary right? It's easily available on Netflix etc. https://dvd.netflix.com/Movie/Jiro-Dreams-of-Sushi/70181716
Random suggestion: instead / as well, take your kid to one of the famous sushi bars at the fish market; for incredibly good wasabi and sushi (it's all about the wasabi, man - the sushi's just a bit of cut-up fish, as wasabi fanatics say!), the hotel will hook you up with exactly where to go. That's more of a "local's" "insider" experience, will also cost you a huge amount of money, and is super-suitable for kids. (Are kids lucky today or what? What a memory.)