As long as the car has been maintained properly then your car should easily make a long road trip without any problems.
Still there's no guarantee that any vehicle will make the long road trip as any vehicle even when well maintained can suffer a break down.
But if you check the car over or have a mechanic check the car over before the trip and fix any issues before they become a problem then the vehicle should make the road trip without a problem.
Be sure to check things such as the tires, belts, hoses, coolant, oil etc and if the coolant is low add more coolant and if the oil is low add more oil and keep oil and coolant with you.
If the belts or hoses look bad then replace them before the road trip to prevent problems because if a belt or hose breaks your car is gonna overheat and leave you stranded.
I took a van that had 400,000 miles on it on a long 3,000 mile road trip and it made the road trip without a problem because it had been well maintained and I like to carry extra belts and hoses with me as well just in case I need them and the tools to change the belts and hoses as well.
So far I haven't needed them but I have them just in case.
Always carry a spare tire with you as well as a jack and the tool to change the tire in the event that you have a flat tire.