Team 7 (Naruto's team) existed for at least while before they took the chunin exam, and they took on a number of missions before taking the chunin exams. I can't remember, however, how long they exactly existed as a team before the exam. How long were they genin before the exam? Is that the normal length? Is there some sort of mission requirement where they have to complete a number of missions before they can take the exam?
The exams happen twice a year. The genins that participate are chosen by their group leaders. So if the group leader is of the opinion, that they are ready at age 6, he sends the genin to the exams, if he's of the opinion that they are not ready yet, he lets them wait. There is no special requirement to take the exams (at least nothing was mentioned), it's just the group leader who decides. This can be seen in chapter 35, when Kakashi, Kurenai and Asuma suggest their team for the exams. Although Iruka protests, he can't do anything against it. That does not mean, that the genin can't decide against it, though. A ninja can't be forced by his group leader to do the exam.
There is no definitve answer to this as no set age or timeframe is given in the manga, anime or on the wiki. Keep in mind ninjas like Itachi who became a chunin at age 10 and kakashi at age 6. (special cases yes but they did become chunin).
So if I were to give an answer, it would be until when they decide to take the exams.
As per the wiki
To become a chūnin, a genin participates in a large examination, known as the "Chūnin Exams".
Again, also as related, keep in mind that not all academy students become Chūnin, so that might apply here too.* No doubt they would have to try again.
And then again there is also this guy.. Kosuke Maruboshi who even though by choice, has been a genin for over 50 years. This could also apply to your question.*