Mumbai International Airport T2 Domestic to International flight but different carrier.

Hi Everyone, I am travelling from Coimbatore to Kuala Lumpur with two different carriers and both are from T2 only. I will be reaching Mumbai by Air India on 8th January afternoon around 4 PM \[ delay considered, if any ). My next flight is on same day at 11.45 PM by Malaysia Airlines MH 195. So my question is after I collect my checked baggage from Air India should I exit and re enter again for check in or I can check in to other airline using International Transfers within the airport. Can any person with valid knowledge please help, because this is my first International Travel.