There is someone on the main thread (I think) doing this diet while breast feeding. I think her baby is older than 9 weeks though. From what I remember she has no problems with supply and her thinking is that this diet is working well for her.
Maybe try doing a search? Or have a trawl through the last thread?
How much weight have you list so far? How much more do you have to lose? I lost nearly all my pg weight very quickly. It may have been the breastfeeding. But many other breastfeeders don't lose as quickly as I did. I strongly advise NOT to diet, if bfing @ 9 wks.