Welcome to the forum!
When you say the "light came on," do you meant the service indicator (not sure if your model had that); or the low oil pressure warning?
If it was the service indicator, that just meant that it was time for a routine oil change.
If it was the low oil pressure warning, that probably meant the oil level was low. Not low enough (yet) to damage the engine, but certainly getting there.
Which engine do you have? As I understand it, the 2.4L turbo "Tigershark" engine had issues with oil consumption; that's probably why the dealer recommended a consumption test.
But it's not like the engine all of a sudden loses all its oil. It's just that it consumes ("burns") oil faster than it's supposed to. (Ideally, there shouldn't be any oil consumption between changes; but normally there is a bit. That's why, even with an engine in perfect shape, you've still got to check the oil periodically -- about once a month under normal conditions.)
Going on a trip is fine. Just check the oil often, like the others have written. Maybe even once a day on the trip. And consider carrying a quart bottle of the proper oil (ask your dealer what that is).
As to why they didn't give you a new engine or new car, your Renegade is out of warranty. Besides, this problem isn't serious enough to do that. If they eventually can't fix the oil consumption issue, then yes -- there might be thought of a new engine. But that's really expensive (for them and/or for you), and they'll want to try to fix the problem first.
