I say check your belts, hoses, and spare tire, top up fluids and inspect for leaks, and go.
Pack washer fluid and a little oil, trans fluid, and coolant just in case, and maybe take a spare belt since that could strand you. I would also recommend against changing brakes before the trip if they're OK now. I like to travel with a trustworthy jack and a 4-way wrench or 1/2" drive torque wrench to make tire changes safer and easier.
More importantly, take drinking water, food, pillows, and blankets or a sleeping bag. Nights are still cold out West, and snowstorms are not unlikely on the high passes this time of year. Also remember your sunglasses and chapstick with sunscreen.
I saw a lot of the country in a 20-25 year-old slant-six Duster, sleeping in rest areas and roadside pullouts and sometimes campgrounds or even motel parking lots. No A/C and power nothing made a day behind the wheel a physical experience, but I didn't know any better until I finally traded up to a car that was younger than me. Your Fit should be miles ahead of the Duster.
The only thing close to a breakdown was when the points burned up. I swapped on my spare carb thinking that might fix it, but no luck. Finally had to call for a tow, but the guy didn't charge me for that since I could limp along behind him. He threw in a set of points and sent me on my way with a new lesson learned.
Regarding high-altitude octane, just use midgrade or premium if you have to fill up in the high country, so you won't have a tank of 85 when you get down low again. The octane starts to get lower in eastern Colorado and New Mexico, between about 3500-4000 feet. This will be most important going into Las Vegas and the Mojave Desert or back out onto the plains on the way home.
Finally, as somebody mentioned earlier, pull over ASAP and sleep if you get drowsy.
I wish I could do a trip like this about now. Have fun, take some pictures, and let us know how it went when you get back. If you're a carnivore, sample the various styles of barbecue along the way.
One more thing: If you plan to drive through some of the national parks, buy the yearly parks pass at the first one. I think it costs about $80, vs. $25-$35 each for a lot of the major parks.