An erratic idle can often be caused by a vacuum leak or a problem with the Idle Air Control valve.
Tests for a vacuum leak can easily be done with a vacuum gauge. As to the IAC there may or may not be codes present showing a problem in that area.
Sometimes, removal of the IAC and cleaning it along with the intake passages may clear the problem up. This is all assuming the IAC or any associated electrical circuits do not have a fault.
With the CEL coming on I would think you should have a code(s) present. As mentioned, get the Jeep scanned and go from there as a starting point.
One more word of caution. You state it’s been 8 months since an oil change and have gone through a lengthy move from one state to another.
You are checking the oil level regularly aren’t you? If not, you’re begging for major league trouble.