I say go for it!
If you are comfortable with it and you select the right weight pop-up than why not? Your not asking it to tow a TT or 5th with a large frontal area that would add considerable drag. Granted with a 4 cylinder, I would opt for a small pop-up, so you can account for gear, occupants, ETC.
After going Tent Camping, using P-ups and TT's, I'm a TT fan myself and enjoy TT camping the best, but if you don't want to invest in a TV large enough to handle a small TT, then why not? At least your getting out camping which is the most important thing!
Let us know how you make out if you get the trans cooler, electric brakes wired up, ETC.