I have a recommendation for you. It's a probiotic superfood. One example of weight gain is an anorexic who was only 80 pounds. In one year she gained 30 pounds and was healthy. This is a miracle if you know anything about anorexia.
I can't post a direct link here so email me: ____@____.com's vegan and packed with amino acids that will build healthy protein cells and also fix any potential gut problems so that nutrient absorption is increased. Amino acids are what she needs, not meat so don't get swayed on that. It could just be that something is missing from her diet. Ideally she would be exclusively breast fed for many months and then started off with fruits. There are healthy and very unhealthy ways to eat vegetarian! The amino acids form protein. Eating meat simply overburdens the body (never mind the ethical reasons, let's just talk health here) and it needs to be broken down in order for the protein to be utilized. Meat is a very ineffective way to get protein and it acidifies the body and leaves a person more prone to illness.
Feed her lots of fruits in their raw state but rinse her mouth after. That will contribute to health, vitamins, minerals, etc with no empty calories. There are lots of junk foods that will pack on weight but that is not healthy weight. The goal should be health, not numbers on a scale.
Let us know how her levels turns out after testing as that will be a big clue for other options. Toxicity could be an issue and if it's lead that would prevent calcium absorption in the bones possibly contributing to this issue as well.
I just saw your response and completely disagree with the allergist about soy. Soy is not really meant to be a human food product. I'm pretty sure they just banned soy formula in the UK. Here's an interesting link I found about breast milk increasing in fat the longer you breastfeed: http://www.medicineonline.com/news/10/6108/Fat-Content-of...
Meat has an extremely high risk factor for many health conditions. Many diseases have been completely reversed simply by going vegan--cancer, diabetes, heart disease, etc. On that note, some vegans will give their children raw goat's milk when they are finished breast feeding.
Interesting comment about attachment parenting. That was actually a direct steal from Jean Liedloff who wrote the book, The Continuum Concept. Awesome book and I highly recommend it to all parents.
Most Indians are very slim so I wouldn't necessarily take the "failure to thrive" that seriously but of course the nutritionist can be helpful. Hopefully she understands a vegetarian diet. Many nutritionists and dietitians are trained by the entities that profit from sales of unhealthy foods like dairy and wheat so keep that in mind if something doesn't seem to make sense. Shop around for someone who is on the same page as you.
From your description she sounds like she's doing just fine, she's just a bit on the slim side. These days with the majority of people being obese being slim looks out of place. Many babies are born obese and unhealthy. Those charts don't allow for much leeway. Children sometimes take after another relative, not just the parents. It could be a grandparent or aunt or uncle on either side whom they physically take after.