Get Off the Unicorn, published in 1977, collects some of Anne McCaffrey's short stories into a single collection. If there is any work by Anne that you want to start with, this ISN'T the one. By all means, judge Anne by a different book.
This is a book that I often debated reading back in high school, and I may even have checked it out of the library. Even so, I have no memory of its contents. On reading it, I see why I would never have read it, or even persevered reading it. The stories in this collection show both their age and Anne's poor narrative ability. The first two stories, in fact, didn't even see publications, and on reading them, it's painful to see why they didn't see publication. Quite frankly, there was nothing engaging about those stories.
To be fair, the stories seem to be presented in written order, so you do generally see Anne's skill increase as the tales progress. A few later stories even read rock solid. Pay special attention to The Great Canine Chorus and Finder's Keepers.
If I had to guess, I would guess that most of these stories date from before Dragonquest, even if they are dated up to 1973. (A written story doesn't necessarily get sold immediately.)
The first two stories eventually resulted in the novels The Rowan and Damia's Children.
If you are a dedicated McCaffrey fan, then you'll read this book anyway.