Follow Your Dream by Marjorie Holmes (1961)

So what's wrong with a girl's wanting to be a veterinarian?  Especially when she's Tracey Temple, who has been loving and caring for all kinds of animals since she was a little kid. Even now, a junior in high school, she really prefers animals to people, and her idea of excitement is being curled up with a good book on hoof-and-mouth disease.

Of course, the male D.V.M.'s want very much to exclude women from their ranks. That hasn't stopped Jane Baldwin, though.  Dr. Baldwin is outstandingly successful, and to Tracey the opportunity to work a whole summer in her idol's hospital is sheer ecstasy.

Not unmixed ecstasy.  Dr. Baldwin has a medical assistant, a young vet-to-be.  Tracey is normally quite at home with boys -- in so many endearing ways they remind her of animals. But Whit is not exactly a boy. He's not even an ordinary man. He is the tallest, handsomest, most terrifying member of the adorable sex she has ever seen.

He is something less than impressed with the clumsy "puppy" whom he derisively calls a canine Florence Nightingale. Yet, for all his sarcasm, he is always ready to help, to teach, to console when the newcomer lets a valuable dog escape -- and to be basically glad, too, that she is the one chosen for the trip to the zoo to help set a lion's tail. In a word, Whit is all bark and no bite, although there's nothing fake about the chunk he takes out of Tracey's heart.

From Dr. Baldwin the intense, gamin-faced girl gains deeper insight into the profession she yearns to follow. Through the glory and the misery of loving Whit, who is not hers to love, Tracey's dream of a career turns into a fuller, richer dream of life. Here, even for girls who shudder at snakes, is a sparkling, romantic, completely intriguing novel about highly animate humans and humorously human animals. (from the inside flap)