Document requirement for a 2+ year old child from India to Nepal by air accompanied by an adult

The Ministry of Home Affairs Government of India Bureau of Immigration details the requirements. The bold/italic added emphasis in (v) addresses your question, that your child must have a photographic document confirming age and identity.

Indian Passengers

Indian nationals travelling abroad require a valid Indian passport and travel authority for the destination country.

The travel authority is normally in the form of Visa, which is obtained prior to the journey, except in case of countries where "Visa on Arrival" is available.

Indians traveling abroad may also note that some countries insist for certain minimum period of passport validity for allowing entry & for this confirmation should be obtained from the Embassy/travel agent.

Indians having the Emigration Check Required (ECR) category of passports require POE clearance from Ministry of Overseas Indians Affairs for certain destinations if traveling on Employment Visa.

For further details see separate topic on ECNR/ECR/POE. Even for re-entry into the country, an Indian national is required to be in possession of a valid Indian passport or travel document issued by Govt. of India.

Identity documents required for Indian Citizen going to / coming from Nepal by Air:

(i) Valid National Passport.
(ii) Photo Identity card issued by the Government of India/State Govt./UT Administration in India to their employees or Election ID card issued by the Election Commission of India.
(iii) Emergency Certificate issued by Embassy of India, Kathmandu.
(iv) Identity Certificate issued by Embassy of India, Kathmandu.
(v) Persons in the age of group of above 65 years and below 15 years would be exempted from the requirement of approved identity documents mentioned at SL. No. (i), (ii), (iii) and (iv). However, they must have some documents with photograph to confirm their age and identity such as PAN card, Driving license, CGHS card, Ration card etc.
(vi) Children between the age group of 15 to 18 years may be allowed to travel between India and Nepal on the strength of Identity certificate issued by the principal of the school in the prescribed performa.
(vii) In case of a family (family means husband, wife, minor children and parents) traveling together, the approved identification documents at SL. No. (i), (ii), (iii) and (iv) would not be insisted from all the family members if one of the adult members of the family has in possession of one of the prescribed identification documents at SL. No. (i), (ii), (iii) and (iv). However, the other family members must have some proof of their identity with photograph and their relationship as a family viz. CGHS card, Ration card, Driving license,ID card issued by school/college etc.

Note:
1. Aadhaar (UID) card is not an acceptable travel document for travel to Nepal/Bhutan.
2. Certificate of Registration issued by the Embassy of India, Kathmandu, Nepal to Indian nationals is not an acceptable travel document for travelling between India and Nepal.
3. The Emergency Certificate & Identity Certificate issued by the Embassy of India, Kathmandu will be valid for single journey for travelling back to India.