Why 3 months? Well the body needs time to recover from pregnancy and the birth. Dealing with a newborn is hard work, often mums don't start emerging from that fog until much later down the line than 3 months. Doing a VLCD and dealing with night wakings and the 24/7 demands of a small person are not very compatible. I am not a health professional but I do work in maternity services and also support women in the postnatal period through the NHS and voluntary roles. I would say a thing to consider is doing a VLCD very early on well may be a risk factor for postnatal depression, it's mentally gruelling and physically exhausting can often leave people with very little energy. The first 3 months is a vulnerable time in a woman's life. It often takes longer than that to get back to normal physically.
Slimming world and weight watchers are much more compatible for the early months, watch what you eat, perhaps calorie count (if you do decide to breastfeed it takes approx 300-500 extra calories a day if you exclusively bf), this is often why women lose weight more easily in the first 6 months.
It might be an idea just to wait and see how you feel once baby is here, 3 months will fly in the blink of an eye once he's with you and I think the 3mth guideline is probably far too soon.