You need to learn 1900 vocab until december, if you do 20 words a day that will result as 95 days of active learning so according to my calculation it’s reachable within 5 months (4,75 precisely) if you study 5 days per week. which means that if you start today you should be ready by end of november for you exam in december.
Honestly I think your best shot is to aim N4 in July. This way you can adjust your pace (since the more words you’ll learn the harder it will be)
as for your plannification of new words : I think it’s best for you to get rid of the N5 vocab asap before starting N4 vocab. You’ll be exposed to new vocab when you do your reviews, make sure to check on them even if they are not in your queue yet.
As a rule of thumb I think it’s best to solidy your base before moving on to the next level.
However when it comes to grammar I think it’s okay to learn N4 grammar even though you don’t know 100% of the words in N5.
You’ll also do the same with N3, N2 and N1…
If you don’t 100% your vocab deck and you keep adding the others you’ll end up with unfinished decks until you reach N1 and that’s gonna be super frustrating…
It’s a long journey until you’ll reach the 10k words required to N1. Keep it up and don’t burn up I believe in you !