It really depends on the page as a whole. Centering is not not-done, but neither is it always a good option. If you're looking at it purely for readability, left aligned text is better (or right aligned if the reading direction is right to left, for some languages).
Justified can sometimes work, mostly for long texts and in combination with hyphenation (hyphenation isn't used a lot in English, but in my language - dutch - it's really common, making dutch texts usually more suitable for justified).
I'd look into books of the same genre, and see what they mostly do (look at books published by established publishers), so you know what the norm (safe choice) is. I would usually only deviate from that if there is a reason for it. If you have a reason for it, it's easy enough to justify the choice if the author/publisher starts asking questions.
For example, if the text is about someone feeling lost, the centered text could add to the feeling of not being grounded anywhere. Perhaps combined with a little more line spacing than you'd usually go for. Or if the illustrations are important, they could dictate where the text can and cannot go.
I can't tell you the right choice without knowing the content. I hope this still helped a bit.
Here's a myfonts newsletter with a few tips that I found surprisingly good: myfonts tips
A rule that may help: for readability, optimal line width (number of characters in a line) is generally 1,5 - 2 times the alphabet without spaces for printed work. Edit: for children, you'll probably want to go a bit less.