Hello, and welcome!
Looks like an excellent choice of book 
You definitely need to know some grammar before tackling a book. I’ve not actually heard of that resource you linked to, so can’t comment on that. Personally, I worked my way through the Genki textbooks. If you’re looking for free resources though, there are things like Tae Kim’s Guide and the Cure Dolly YouTube channel (it’s the most horrific thing you’ve ever listened to, but advocates swear you get used to it / recommend speeding up the video / turning off the sound altogether and using captions).
How long it will take before you can read that book will depend on how much time you have available to study, and how quickly you learn 
we put together a vocabulary sheet as you go, so grammar is actually much more important than vocabulary in this case (it doesn’t use many kanji either).
If you’re really determined to set that as your first reading goal, you could consider buying it, and then periodically having a go at reading the first page or two to see whether you’re ready to tackle it yet!
As reading practice / milestones in the meantime, you might like to look at other free reading practice you can get online, such as Satori Reader, NHK News Easy, the EhonNavi children’s book library (there’s a thread dedicated to it on these forums), these free graded readers, etc.
I’d really recommend taking a look through this thread, though I may be somewhat biased 
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