Spaces between the words when writing in kana is quite normal, incidentally; if there is romaji in your text book then take a piece of paper, cover up the page and read a line at a time so as to avoid "cheating".
Lots of people decide they want to do this (e.g. learn from kids books). I've never seen anybody get very far with it. (Usually something like "I thought kids books would be easy, but I can't find ねちゃう in any dictionaries, help!") Manga can make a good starting point once you're ready to go into real text, because the images help with context - but not at the very start.
The problem is, children's books don't use necessarily use "beginner" grammar/vocab. Kids are going to easily recognise things like たべちゃだめ which won't even be taught in beginner texts, and words like "skip" and "hop" (or "skippity-hop!") which aren't really a high priority for a second language learner. (Not to mention the possible hurdle of running across the equivalents of "pee pee" and "choo-choo-train", without having any way of knowing which words should not be used by anybody above the age of seven).
Think about something like Dr. Seuss or your example; a non-native speaker is not necessarily going to immediately recognise "Spike" as a relatively common dog name as opposed to an ordinary noun, and "see Spike run" may not be a grammar pattern a beginner will recognise. I'm trying to think how to put it in Japanese now: スパイクが走ってるのを見て!, perhaps? It's also not that useful as a sentence pattern; I don't think I'd ever say "See (name) (verb)" in real life. ("Look at him go!", maybe).
If you do want to have a go there is plenty online. Jericho's link is good, but you might also try:
http://www.nikonikoehon.net/picturebook1/index.html
http://www.nikonikoehon.net/picturebook2/index.html - cute "animated" picture story-books (some with English-translated versions). If you can parse the descriptions (e.g. sentences like: とてもいい においがする フシギな木の実がありました。) then you'll probably be okay with these.
トップ - Kibiehon - possibly the best book ever (this site has example extracts of various picture books, this just happens to be my favourite).
As an alternative to kids books, I think one simple source of reading material is something along the lines of this:
動画を見ながら折れる『おりがみくらぶ』
You will need to know things like: て-form of verbs, verb stem + かた means "way of/method of", some origami-related vocab for which you should read this one first:
無題ドキュメント . However, there's no slang/dialect, no cutesy sound effect words, and so on. Plus, you get to make origami.