@christopher000 My second had very fast weight gain early on and nursed a lot. Both the pediatrician and the lactation consultant thought it was great, warned that her weight gain would probably be slow later on (it was,) and said to nurse on demand. Nursing on demand if possible is standard advice for quite a bit older babies.
If it is working for you, I think you should keep doing it. If the frequent nursing is a problem than you can try other things, but it doesn't sound like it is a problem for you.
Also, I don't think your pediatrician is very knowledgeable about breastfeeding. If you are uncomfortable with going against her advice, I'd ask if there was a medical concern had with comfort feeding or get a second opinion. Babies definitely do cluster feed after 4 weeks. It does settle down as they get older, but I think 6 weeks is a pretty common crazy cluster feeding time.