I am trying to build a system that will be able to process a record of someone whistling and output notes.
Can anyone recommend an open-source platform which I can use
Well, you could always use fftw to perform the Fast Fourier Transform. It's a very well respected framework. Once you've got an FFT of your signal you can analyze the resultant array for peaks. A simple histogram style analysis should give you the frequencies with the greatest volume. Then you just have to compare those frequencies to the frequencies that correspond with different pitches.