Given that the result of an FFT can be interpolated (possibly very accurately using Sinc interpolation), the number of FFT points required to estimate the frequency depends on the signal-to-noise ratio of the data containing your signal, and the type of resolution you require (peak separation, or peak estimation).
In the extreme case of zero noise or other interference, only 3 or 4 non-aliased points are required to exactly reconstruct a pure sinusoid and thus estimate its frequency.
I'm just wondering if you have a reference I can look up for the details about the quantitative relationship between the limit of signal to noise level and allowed data points for the FFT. That is, if I have a data set of 10 which has a signal to noise (S/N) level of 100, is it good enough to reconstruct 3 pure sinusoid and its frequency? and how about the case of S/N level of 10?