As long as it's in good shape I don't see why not. I've driven older cars than that on longer trips. Change oil and filter, air filter, gas filter, maybe spark plugs too if you don't know how long they've been in there. Check the tires, how old are they? (Check date code. You don't want to be doing high-speed long-distance driving on old, dry-rotting tires.)

Since you just bought the car, was it checked out by a mechanic? If not I'd have that done first o reduce the chances of trouble on the road.

Since it's new to you, I'd drive it frequently to what I call "prove it out", make sure the car proves that it's in good shape by doing well on local trips before setting out on your 7 hr. trip. Check for condition of the fluids and for any leaks (oil, trans, diff, brake, power steering etc.). Check air filer, plugs, tires. But it is nearly 20 yrs old, so anything breakdown is possible, heck can and does happen with newer cars too. Prepare for the worst, hope for the best.