We often towed our heavier 16' Scamp with our Outback before we retired. Since it is heavier than a 13' we had to work to get the
weight and balance right, even removing one of the two
propane tanks when using the Outback. I actually preferred using the Outback over our Dodge Dakota so would use it on local lightly packed trips, or if we knew we were going to do a lot of solo driving at our destination.
We would still be using the Outback except once we retired our travels required both
propane tanks and more cargo, so our weights went above the 2500/200 we limited ourselves to. (Outback limits were 2700/200 but have increased this year to 2700/270 or 3500/350 depending on trim level).
Since we traveled mostly close to GA, the highest hills were crossing the Smoky Mountains at Newfound Gap which is high but not very steep, and also US 441 in GA with a 7% grade. The Outback handled that with our Scamp 16 with no problems up or down.
Since the 13' is lighter I suspect you will have no problems pulling it with the Outback, just make sure you follow the guidance in the owners manual regarding steep grades above 100 degrees and braking requirements.