Mine has been doing the same thing. I usually change the oil every 5,000 miles, but I haven't been able to go that long because it uses it so fast. I just had the oil changed at the dealer after 4,000 miles…it was down from 6 quarts to 3 quarts. I have no visible leaks anywhere. The dealer said they would contact Dodge to see if they've heard anything. If they don't get a response, then I'm going to contact them.
Update: The Dodge dealer took our Journey and checked it out based on things to look for from Dodge. PCV was fine, so was breather and intake. They started it up in the am (cold start) and saw a little smoke out the exhaust. They ended up replacing all the valve seals (24 of them). Covered under powertrain warranty. Guess we'll find out in 4,000 miles if it's fixed.
Another Update: Replacing the valve seals did nothing. It was still down quarts after 4,000 miles. Dealer wants me to bring it in every 1,000 miles to look to see when it starts using it. Now I need to find time to do that. :-(