Here are some conservative estimates (purely my opinion):
Land at 3AM.
Immigration, Baggage pick-up, Customs = Approx 1 hour total. (This might be much faster sometimes..... and you could get out in 20 to 30 minutes).
You are outside secure zone by 4AM.
At that time of the day it should not take very long by taxi on a Saturday morning to get to the domestic terminal ..........however:
The airport provides a free shuttle every 20 minutes as well:
http://www.newdelhiairport.in/terminal-transfers.aspx
I would simply use these shuttles.
If you definitely would like a taxi...some people on this forum prefer "Meru cabs". They are reliable. They should have a counter in the area where you exit the secure zone (after Customs clearance).
I have not used the arrivals lounge at DEL. However, some people on this forum know much more about it. I would recommend getting your shower, etc in that lounge.
You need to get to the domestic terminal by 645AM or so...for an 850AM departure. So, you could easily spend an hour or two in that lounge.
Plan to leave the international terminal by 6AM to 6:15AM...you will be fine.