Bubba, First of all
to the forum. Next, I'm sure you're and your family will enjoy seeing the southeast in your new Outback. It's a great trailer and you chose a very spacious floorplan.
Now, to answer your question. That is one of Outback's largest models. It weighs in at almost 8000 lbs empty, by the time you add supplies, camping gear, clothing, food, entertainment equipment, bedding and the "tools and toys" we all find we need to travel, you're going to add at least a thousand pounds or even more. Remember that the 7440 shipping weight does not include propane, batteries or the weight of the hitch.
In 1993, we bought a Holiday Rambler 34 CBFK. At the time I had a 1987 F150 with a 5L engine, 4 speed automatic transmission and about the same rear end gearing that you've got. In fact, we bought it from Cenla Camping Center in Alexandria. When we picked up the trailer, we headed down MacArthur drive to I49 south just to see how the trailer towed (remember it was empty and brand new). We were really unable to get above 60 MPH and the truck was really struggling. The first exit off I49 south of Alexandria is LeCompte, and back then, Ken Brady Ford sat just north of town. They had a 1993 F250 with a 7.3L diesel and HD automatic transmission on the lot. It fortunately matched the trailer color.... After some quick negotiations, they installed the brake controller and we towed back to Alexandria with our "new truck and trailer"
The reason I added my experiences is because I'm thinking that once you get that much trailer behind your pick up, you're going to see very much the same performance. You may be able to tow fairly well on flat ground, but every overpass you climb is going to put you in a downshifted, high rev climb. I'm thinking that you're not going to be able to tow with any satisfaction with your current truck.
Now, also remember that they 800 lbs tongue weight is the empty weight, you should be between 10 and 15% of the total trailer weight. That means you're really going to be much closer to 1000-1200 lb tongue weight. With your wife, the two girls and yourself in the cab, you are most likely going to be over your truck's payload as well. And that's before you put any cargo like firewood, generator, fuel, bikes, etc in the bed of your truck.
I'm inclined to think you should seriously look at a bigger truck (in the 3/4 ton range) for a trailer like that.
Again, welcome to the forum, look around, you'll see that we've got pages of documentation discussing exactly what you're trying to do. Look around, see what other's have found about their towing limitations and hopefully you'll benefit from their experiences.....