It doesn't really matter if it's oat, as long as you're not mixing types. Last time I did a JK, It took (if memory serves) about 2.5 gallons.
I would question the competence of a dealer who tells you to use water in your coolant system. The minerals in tap water tend to build up in the system. There's not much flow through a clogged system. You need to either buy distilled water or buy the premix 50/50 coolant. I buy the 50/50.
The bigger issue is burping the system. I can't tell you how many people have come here to ask about overheating problems that were due to their failure to burp the system properly.
You need to lift the nose 5-6". Fill the system, start it up, turn the heater on full hot, and wait. As the engine temp increases, the thermostat will open, and the coolant level will drop. Keep adding coolant, or you're going to suck an air bubble into the system.