I think once you know basic grammar and sentence structure your pretty much set.
Of course if you already have a good vocabulary then that's also a bonus.
For me it was about 4 - 5 months in that I attempted to use Japanese only (I didn't do it much but I tried when I could)
I've been studying now for a total of roughly 7 months.
Computers make the job of studying monolingual a lot easier too.
I have a paper dictionary with furigana in it for kanji that I can't read yet but when i have a computer nearby i don't really use it, just because looking up kanji is faster on a dictionary website.
Basicly whenever you feel comfortable reading Japanese only, you could start to try monolingual study, although it will be difficult to start with.
For example do you feel comfortable reading this:
盗む Dictionary Link
to figure out what the verb 盗む【ぬすむ】 means?
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Now although this wasn't really part of your question i feel as though I should explain why you can start at such an early stage, since even at an early stage of learning it's easy (for me atleast) if you just
break it down.
If your not interested in reading my explanation just skip it
For example if we take the first entry of
盗む Dictionary Link:
(1)他人の物をひそかに自分のものにする。とる。
I already know the words 物, ひそかに, 自分, する, とる (とる alone makes this verb quite obvious)
I don't know 他人 so I just have to look that up as well, although I do know the kanji 人 so I can take a guess it's going to be to do with a person, and the rest is just basic grammar, の, に etc.
So I'm not training to be a translator or anything so i don't care if my translations are spot on, as long as I understand the true meaning, so my translation based on the basic grammar and words I know would be something like:
(他人)'s thing, secretly, one's own thing. とる = to take
(don't ask me to tranlsate にする here, like i said above, i get it's meaning just dunno how to translate it)
so lets look up 他人:
他人 Dictionary Link
the entry I found easiest was
(3)見ず知らずの人。親しくない人。
my shady translation once again was:
person of strange. not close person.
So i came to the conclusion it meant
stranger/person you don't know.
so basicly: 他人の物をひそかに自分のものにする。とる。 - to secretly take another persons belonging's (in other words
steal)
yay! we just looked up a word using a monolingual dictionary and only basic grammar!
Of course studying
grammar in only Japanese could require more knowelege of the language first but it's still doable I think.
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Sorry for the long post, not all of it was exactly what you asked for but hopefully it will help you understand why i think monolingual learning should be done as early on as possible, or to word it differently, why I think it doesn't take long at all to be able to study monolingual 