I got back from a 3600 mile round trip from Wisconsin to Corpus Christy, TX just a few days ago. I pulled a 19' TT with my 2013 Silverado 1500.
This is my suggestion. Concentrate more on preventing a problem than reacting to one. Your good to still be ready if it does happen, but try to prevent it from ever happening in the first place.
Your rig sounds great. Enough truck for the trailer. If the trailer is new, you are probably good to go but if not, and even it if it is, you should check these things before hooking up. Tires: What are the age of the tires? If they are more than 6 years old, they should probably be replaced. Do they have any cracking or other signs of undo wear and aging? Even if the trailer is new or the tires were purchased recently, check the age stamp on them. Sometimes you will be sold three or four year old tires. Even if they were not used, they still age and deteriorate with age.
Check the brake system on the trailer. Don't just assume it is working. It sounds like you are going to be doing some mountain traveling. This is a must. Check the breaks themselves and the system for proper operation.
Also, the wheel bearings. Make sure they are not worn out and if they have not been physically inspected this year, then you should pull the hubs and inspect and regrease them if necessary. A quick easy way to check the bearings is to put the wheel up on a jack so the wheel is off the ground. Then grab the wheel on either side and try to rock it back and forth. If it moves more than a very slight bit, it needs attention.
Make sure you hitch, chains, hitch pin, light hookup, emergency trailer brake and other hitch components are adjusted and working correctly.
And, since your truck is going to take the brunt of the wear and tear, make sure it is properly prepared. Transmission, engine, and other fluids topped off and within service intervals.
Then, go ahead and consider planning for the unexpected problem should it arise. During my trip last week, I had a blow out at 72mph on my single axle trailer and it wasn't a great experience. I got over quickly and was able to swap out the spare within 20 minutes. I had 100 miles to my next destination and then got the two original tires replaced and the spare back on the spare mount and was good to go. Slight undercarriage damage to my trailer but nothing bad. I had the tools to make the change with me. My mistake was not having new tires put on before the trip. They were 5 years old which isn't bad, but last winter when I put my trailer up for the winter, I let the pressure drop down to about 20PSI in them over the winter. When I aired them up in the spring, I noticed some cracking where they sat nearly flat. But, I disregarded it and they were fine for the summer local camping trips and even the first 3000 plus miles of my long haul in Texas summer heat and everything. But just south of St Louis, BOOM. It was my fault for sticking with my clearly compromised tires that were nearing the end of their life span. I am sure I could have gotten away with my short summer trips at 55mph for another year or two, but the long hot trip was more than they could handle. Lesson learned....one you would be better off learning from me than from your own experience.
Good luck with your trip and enjoy it. I stayed at military base camprounds on my trip. If you have access to military bases, I highly suggest you checking into them for your trip. Most are $20 or under for full hook ups and very well kept up.
Post back when you get home and let us know how your trip went.
Oh, check your hubs by hand for excessive heat (indicating bearings going out) at each stop. The hubs should be warm but not hot. About 100 degrees or so. Not uncomfortable to the touch. Also, check tire air pressures regularly while traveling. Each fill up at the gas station is perfect.
If you get TPMS monitors for the tires you are set there, but if you like gadgets and want a quick, easy and accurate way to check for excessive heat on the hubs, you can get an infrared temp gauge that you simply point at the hub and it tells you temp. They are under $25.00.