Bear in mind, my 'road trip/hauling' truck is my 290k mile, 2001 Ram 2500 Cummins. I travel a little "heavy" when it comes to roadside safety items lol.
My travel pack for trailering includes:
1. floor jack
2. trailer spare(s) - check your bolt pattern, and your load rating!
3. 20v 1/2" Dewalt impact gun with 2 charged batteries
4. 4-way lug wrench (in case of DOA batteries)
5. bouquet of HD zip ties - I grab a handful, then zip one around them to hold them in a bunch.
6. cheap-o set of box end wrenches - I have a set I bought at wallyworld, it's like 39 wrenches, SAE and metric, and they're "disposable" so no guilt if they break or get lost
7. dikes (cutters)
8. vice grips
9. about 10' of residential 12/3 solid core wire. not to use for power, but as heat-proof zip ties if needed ("mechanics wire")
10. jump box
11. tire rope plug kit
12. 12v compressor
13. fluids (oil, trans, coolant, etc) - at least one bottle of each
14. bungee cords
15. 1 or 2 spare HD ratchet straps
16. $500 extra cash (never know when an ATM is gonna take a ****, or your card will lock up)
17. Springfield Hellcat with 2 spare mags (permitted)
18. spare fuel filter for my truck - I have a gauge on my fuel pressure and it if starts reading low, a filter swap is cheaper and easier than a new VP44!
19. cordless screw gun and a box of drywall screws, and a box of self-tap sheetmetal screws
20. combo-tip screwdriver (+, -, torx)
(21. when making a motorcycle-grabbing trip - 1 or 2 2x8" boards as ramps - not bad to have with a rental trailer, either, actually...)
I did much the same when I bought my Charger a few years back. MD to FL to pick it up, behind my diesel. I had a home base in FL (family home), and I know the run - 11h down I95, 11h back. Do it all the time, so no surprises there. Check for construction - Waze is actually pretty good for that, since its crowd-sourced and will show you any delays/reroutes/etc before you get there. Plug in the route the night before, and it'll populate all the trouble spots for you so you can decide which of the alternatives you want to use.
Anyway, when I went to get my Charger I did a 'local' rental on the trailer - rented it near my house, returned it there 3 days later. Towed it down empty (good time to check the trailer, BEFORE putting my new baby on board!), towed home loaded. One of the retractable ramps decided to come free and extend itself while I was driving, so once I got pulled over and got it stowed back in the socket under the deck, I used one of my ratchet straps to secure it so it didn't fall out again.
Check the trailer when you pick it up. It should have 2 chains that go to your truck's receiver, along with a 4 pin plug for lights. It should have a surge brake (telescoping tongue) so make sure it operates. There is a safety-catch (for backing up) - make sure it operates properly and doesn't lock the tongue at random. Check the lights, hooked to YOUR truck to eliminate any issues. It should have two chains that hook to the car's chassis (the Charger). Check the ratchet straps, make sure they operate and latch. Have spares in case they don't. Take a small padlock, to lock the trailer tongue to your hitch ball. (I cheat, I have mounted a backup camera on my truck that catches the trailer tongue, so I can look at it anytime - I have the camera wired to turn on anytime my tail lights are on). For wheel bearing concerns...tow it about 20 miles empty, stop, put a hand on each hub. They should all be cool-to-warm. If one is hotter than the others...go see UHaul asap. Either a brake is dragging, or a bearing needs grease.
When you load, it should have front wheel "net" straps to hold the front wheels. I always over-compensate (especially when towing my Charger) - I use them, THEN I do an X-pattern forward from behind the front wheels, connected to the frame, and I do an X-pattern rearward from in front of the rear wheels, connected to the frame (NOT the diff). Strapping only the wheels to the trailer lets the Charger bounce on its suspension, on top of the trailer's suspension...and that can add to trailer "wag" in certain situations; I prefer front and back FRAME connections, which preload the suspension and help cut the bounce. I strap it, drive 5 or 10 miles, and check all straps for tightness. Usually if they're good after 10...I let it eat the rest of the trip, and just drive.
I do have my truck outfitted with a bluetooth stereo, so I don't have to worry about earbuds, and I have a charger cord hardwired. I have a magnet mount on my dash (below the windshield so I don't block any sightlines) so I can see my waze maps as I drive. I keep an eye on my fuel pressure (it's a 24v thing), and did actually replace mine in FL before coming home because my pressure was a consistent 1-2psi low on the way down. I also carry a tire pressure gauge (digital - forgot that in the list above) since I don't have TPMS on my '01.
And, if you wear contacts...take your glasses, too! I never know when I'm going to have to change mine due to blurring...
And since you're traveling through some "badlands"...take 5 gal of diesel along too, just in case!
Safe trip, and enjoy the new Charger!