It sounds like you have
dt = 1/2.5e6;
N = 600/dt;
N samples is that correct? To achieve a frequency resolution of 0.001 Hz with a sampling rate of 2.5 megahertz you need
1/(0.001*dt)
samples, which you don't have. Padding the fft does not increase your frequency resolution. That is determined by your sampling rate and the number of samples you acquire. Padding the fft() only interpolates the frequency grid.
So in short, no, you don't have enough data for the DFT to have 0.001 Hz resolution, let alone the short-time Fourier transform for which you would have to segment your data.
