How long do you think you will have between finishing Genki I and October (which is when you estimate you’ll be able to get Genki II)?
From what I’ve heard, Genki I covers roughly all N5 grammar. That’s definitely not ‘nothing’, but it’s relatively simple grammar that will probably only cover basic factual statements. You probably won’t be able to read very interesting books with just Genki I grammar.
Hahaha. Truth is, it depends on the particular book you’re looking at. The Japanese equivalent of children’s picture books (if it exists, because I’ve never tried looking for one) should be quite readable for you, though you’ll definitely need that dictionary. For instance, in my opinion, Kiki’s Delivery Service feels like a children’s book because it’s grammatically fairly simple, but it still has a lot of descriptive vocabulary, which means you’ll keep having to open your dictionary, even if you might not need as much help with the grammar. Also, the real difficulty when it comes to reading Japanese is knowing what all the different particles do and what sorts of ‘common structures’ to look out for. The sentence structure is completely different from the sentence structure used in modern European languages, so it’s easy to get lost without an idea of what more complex relative clauses (i.e. clauses that describe nouns) can look like.
Honestly, I think it’s more helpful if you use your experience with the 3rd edition of Genki I to gauge whether or not there will be major changes between the 2nd and 3rd editions of Genki II. If you feel that the gap was huge for Genki I, then you’ll probably want to wait for the 3rd edition of Genki II, perhaps while borrowing the old edition from a library or via Kindle rental. Otherwise though, there probably won’t be too many issues getting Genki II now.
EDIT: @seanblue I see that I’m not the only one who thought of 魔女の宅急便 (=Kiki’s Delivery Service)! And I’m glad to see I didn’t misjudge the level of difficulty of the book. However, yes, so, @Gentarozzo, as you can see, it’s possible, but it’s relatively difficult without help. I’m fluent enough to read NHK news articles (the ones for Japanese readers) with a bit dictionary checking and to watch my favourite anime without much help from subtitles (maybe 70-80% of the words caught, partly because I know the story), and the first time I opened Kiki’s, I needed a dictionary on the first page because the writer’s vocabulary was very descriptive, even if the grammar was quite simple.
If you want, you can try joining one of the book clubs on the forums, but if you’ve decided to wait for the next edition of Genki II to come out, then you’ll probably want to read something like Tae Kim’s Guide to Japanese while waiting. It’s free and fairly detailed, and all the explanations are in English, along with relatively simple example sentences. You can also try reading NHK News Web Easy articles, which are simplified news articles that will allow you to see relatively simple grammar in action (probably slightly above what you’ve seen in Genki I). There’s a thread I help out with on the forums where we attempt to understand and translate these articles. Most of the people involved are beginners who started out on Duolingo (which doesn’t teach much grammar, as you probably know) and worked their way up. More advanced members do their best to help other members decipher confusing grammar points or sentences. You’re welcome to join us.