A car with 300,000 miles or more is safe to take on a road trip as long as the high mileage car is in good condition and is running properly.
The car should have no issue with driving on a long 3,000 mile road trip or a 6,000 mile round road trip.
It would be the same as driving the car around town or in the same state and covering those same 3,000 to 6,000 miles.
If you expect your car to last longer than the 300,000 miles then driving it on a long road trip should be no problem.
I have a truck that has 700,000 miles on it and it's been maintained properly and I take it on long road trips pulling my travel trailer behind it.
If it had not been maintained then I would not take it on a long road trip.
Long road trips are better for your car than short trips anyway because your engine gets up to temperature which helps keep moisture out of the oil.