I recommend the following procedure:
1. Immediately get a written opinion from the paediatrician that there was negligence. The case against the doctor cannot proceed in the absence of a written adverse opinion against a doctor by another
doctor.
2. It is strongly advised that you should get a copy of the medical case sheet from the hospital concerned. The hospital is bound by law to provide it within 72 hours of receiving a written request.
3. You should get the hospital case sheet as well as the OPD record examined by subject experts and get a written opinion about any negligence etc. You should not expect to have such opinion free.
4. You should file a complaint in the concerned consumer district forum on the basis of the expert opinions obtained. You can do so on your own. However, it would be better if you engage a lawyer.
You can file the complaint up to two years after the negligence. There is no court fee in a consumer court, except Rs. 100-500 as a token charge. You can expect a decision within 1-3 years.