I self-published a children's book a few years ago. It was aimed younger than yours - probably 3-6 years. It did alright for a while (not as good as my novels) but to be fair i didn't really do any marketing...it was more an exercise in getting it in some form so it wouldn't be lost forever (in a future that aint what it used to be lol) so i had someone illustrate it and put it on Amazon. I personally would always go self published with any future books (when I get around to finishing the dozen or so that are underway - too many irons in too many fires to rush things out) for a few reasons.
I know a few published writers and i know what they went through in both time and money to get published, and they are making a reasonable living from it, but I can put out a book on Amazon with a paperback version in about an hour and for a fraction of the cost it would be to send out prospective letters, which means there is money left for some targeted advertising. Plus there's the factor of having full control over your book, the lack of multiple page contracts to sift through and try and work out who is doing you over on which page. If you're willing to put in the graft, get your work in front of the people who are going to buy, then there's nothing you can't do yourself. I sell video greetings and when i started I had no reviews, no website, and a whole load of competition...two years on it's projecting about 10-12k profit this year. A bit of grit, determination, going against the grain every now and then and just plugging away until you get where you want to be, you get there with or without agents/publishers.
Sorry that was a bit longer than intended. Good luck with the book i know how competitive the teen market is
