I think the Surly Long Haul Trucker loaded touring bike is considered a good bike for touring. Most loaded touring bikes are good. They all perform the same task and all more or less do it equally well. Its not really complicated. You want to go on a loaded tour. So far you have only used the bike for unloaded riding. Here are a few suggestions to consider.
Tires: For unloaded riding, you want light, thinner, more supple tires. They make the ride more fun. BUT for loaded touring you want heavy duty rough tough thick heavy tires that are indestructible. So get some tough tires for loaded touring. They will suck for riding until you get 50 pounds of gear on the bike and are in the middle of nowhere riding through glass and thorns and nails.
Shifting: The LHT comes with bar end shifters. Fine choice. Some love them. Until they ride a bike with the new fangled modern supposedly delicate and breakable STI shifters. Then they want to take a hammer to bar end shifters and pound them into junk. You could make your riding, loaded or unloaded, more fun with STI shifters.
Handlebar tape: You might want to put two layers of tape on the bars to make them more cushy and comfortable. But if you have small hands then the extra thickness may make the bars harder to grip. So don't do it.
I'll assume the gearing on the bike is adequate right now. And the saddle is comfortable. And the reach to the bars and bar height is right. What pedals do you use? I favor SPD pedals and sandals for riding. Nothing is as comfortable as that combination. For fun before your big trip you might want to replace the chain, cassette, chainrings, cables, brake pads. And oil everything up very well. But you probably don't need to replace all those parts. Bike will work fine as is. Just replace the parts when they wear out or break. No need to waste money on new stuff when its not needed. I'll also assume you already own racks and panniers that work well enough.
There really isn't any single best improvement, modification, investment you can make to the bike for loaded touring. It works well enough as it comes from the factory. Any changes are minor. Your question is just like a Toyota Camry owner asking what is the single best improvement I can make to the car? How can you improve a car that runs perfectly for 300,000 plus miles and never ever breaks down? And rides and handles fine. Paint flames on the side of it?
