You won’t get much in my area for $3,000.
And I agree that modern cars are far, far safer and more reliable that anything out of 1951.
However, if you drove “all the the way to Chicago”, that suggests to me that you’re in the rural midwest. Her desire to be a vet sort of reinforces that suspicon of mine. And, frankly, when I was out there 40+ years ago there was a lot of rural roadway still in use.
I have mixed thoughts. If this is in good operating condition, and the area you live in is rural, I’d suggest keeping it for her. It’ll probably be safer than what you can get for $3000. Use the money you would have spent to help her through vet school. Then, if she wants to, she can sell it. Millions of young kids grow up in the rural midwest with vehicles like this and they do fine.