Hey sweetie,
Have a friend who was on this diet and yes it is incredibly restricted, however I think you could continue to breastfeed successfully, but you will need to monitor your calories, calcium, protein intakes etc. If I were you I would probably contact a nutritionist so that they can help you to work out meal plans, snacks etc to make your days easier....
There are several mums on here who are on elimination diets (very restrictive) because of their LOs food allergies and intolerances, and all their bubs are doing well....you just have to be VERY organised, and have good support.
Hugs sweetheart and good luck
xxx