Hi ikonos,

Upon arriving into BOM you would have to clear immigration, collect baggage & clear customs before taking a "inter-terminal" coach to the Domestic terminal 1A (Kingfisher operates from 1A). The coach service is free, but operates around every 20-30 minutes.

Kingfisher First offers you complimentary access to the Carnation lounge (located opp gate A2). The Lounge opens at 04:00 and offers a decent breakfast spread, workstations with internet connectivity, TV & newspapers etc.

There is also the AMEX lounge "located inside" the Carnation lounge, but i am not sure of their hours of operation / offerings as I am not an AMEX member.