More about Traveling SOLO
Contrary to popular opinions, and this is an echo of what Bob and Gen have said, traveling solo is no problem. Just remember, about 89% of the people you come across are just friends you haven't met yet (yes, there are still good people in America). Just remember: Be aware, no hitchhikers, and don't hitchhike yourself (certain situations of course may dictate otherwise, but thats a personal judgement call).
My advice for your car is to have its routine servicing done on it just before the trip. Have the fluids checked and filled, oil changed, tires examined, brakes inspected, etc. That's the best to making sure your trip won't end up a call to me (for those who are familiar with RTA boards, I work with AAA road service).
Personally, I like driving solo, it allows me to just take what ever road I want and not have any "backseat drivers".
Just remember a few more things when on the road- 1) Know where you are. 2) Keep your cell phone charged (pack or buy a car charger, very important). 3) Know someone you can call if you do find your self in trouble.
But other than that, you really don't need to fret. You drive solo everyday when you commute don't you, driving long distance is no different.
Again, 89% of the people out there are friends you haven't met yet.