No, there is no such feature, since it wouldn't have any effect. There is a short Help Center article What should I do if no one answers my question? which may or may not help you in this case, but posting it at a different time would have no effect. When you're awake, there may be less visitors, but there are also less new questions competing for attention, and both effects cancel each other out.
I've done some research a while ago on Stack Overflow question views, of which the conclusion was
The number of views for a question is independent from the moment of posting.
On Music.SE we have less data to work with, so I modified the query a bit:
The horizontal axis is the 'hour of the week' - due to SQL Server peculiarities it starts counting at 24. You see the daily peaks in the number of questions around 18:00 UTC; note that there's no such pattern in the number of views.
Finally, even if such a tool would exist, it has the disadvantage of not being able to react to comments/answers soon, which might be necessary to improve your question.