Why did Daniel Defoe not write about the plague until some years after it had ended?

This question requires quite a bit of speculation on the part of readers and historians, so there may not be more than an educated guess at an answer.
A few things to consider are that Defoe was too young when the plague occurred to have extensive knowledge of it, that he wrote the work as a fictional diary, and that much of the details have been traced to historical records, accounts he may have heard from living relatives, and the actual journals/diaries of famous writers who were adults at the time of the plague.
A simple answer to the question is that Defoe, born in 1660, would not have been old enough to write with such eloquence until quite a few years of education later. He would have been only four or five at the time the plague occurred.
Another, more insightful question may be what was going on at the time, half a century after the plague, that made it an item of interest to his audience. It clearly enjoyed enough popularity to have made it a part of the canon.