I agree with Earthliŋ's answer, particularly about looking for books with spaces between words, but I'd like to add a few more thoughts and point out some specific issues.
There are different levels books aimed for very young children. First there are baby books, for children who are just learning words. These will usually just have one or two words with each picture, e.g., かー and/or ぶーぶー. The first is just the word for car, and the second is the sound it makes. In general, Japanese children's books use a lot of onomatopoeia, most of which can be found in dictionaries, but in simple cases you can guess the meaning from context. These should not be too hard to read.
However, baby books are probably not super interesting. A big issue when reading simple story books, in addition to a lot of vocabulary you wouldn't learn in introductory textbooks, is the use of slang and things like word play. First, most (but not all) introductions to Japanese start off by teaching you polite Japanese, which is not how kids learn (familiar, casual Japanese). So kids books will use a lot of casual Japanese. Second, there's a lot of slang in spoken Japanese, just like in English, and this will appear in kids books as well.
(e.g., しています meaning "is doing" is している in normal casual Japanese, but often pronounced and written as してる.)
As for finding gaps between words, even as you progress it takes effort. One thing you could do is use a good online dictionary (or tools like rikai-chan), preferably one that will recognize verb conjugations, as you will run into a lot of conjugated verbs you need to work to try out various possibilities to find the root of (I think jisho.org, at least the beta version, may do this for you.) This helps, but you may still need to try several possibilities to figure out what the words are. It is also much easier to determine where words begin and end when you have a good sense of the grammar, which you'll need to make sense of what the words mean when strung together.
Anyway, I think reading children's books is great, but assuming you mean simple story books, you may either want to wait until you learn a decent amount of grammar (e.g., maybe after going through 1-2 introductory books) or start with bilingual children's books. There are a lot of these available in Japan (though I don't know if they'll be easy for you to get) aimed at teaching Japanese kids English from a young age.
I probably didn't start reading children's books until covering roughly 1-2 semesters of Japanese, and even then learning to read children's books was a very slow process for me (mainly due to vocab, grammar and slang), so you need to be patient. Treat it like a research project. Invariably, there will be times when you get stuck, and then you can ask someone you know or ask on here for specific questions.
