Yes Pilates is great for prolapse because it strengthens the muscles of both the pelvic floor, diaphragm and core so that the support structure around the pelvis all works together again.
Here's where I would suggest you start -- this page has a Self Assessment video to help you choose the series to begin with. You'll want to start with the PrePilates series first:
In order to make sure you're engaging your pelvic floor correctly, visualize that you are picking up a marble with your undercarriage. Hold onto the imaginary marble throughout the exercise. If you can't, go back to a version of the movement that you can hold the contraction and repeat that version for several days, then try the next movement again. It may take time for the muscles to connect and do what you're telling them so be patient.
Hope that helps but I'm here if you have more questions.