I've always loved the classic 'The Last Battle' from the Narnia series for its poignant take on loyalty, though the unicorn Jewel is more a noble companion than the star. For a story built around the bond between a unicorn and a child, 'The Unicorn and the Lake' by Marianna Mayer comes to mind—it’s quieter, more of a fable, but the friendship feels ancient and pure. Honestly, most unicorn tales lean heavily on the 'magical creature as guide' trope, which can get repetitive.
If you want adventures where the friendship is the engine of the plot, not just a decoration, the middle-grade series 'Unicorn Academy' is probably a better bet. It’s lighter, sure, but the girls and their unicorns actually solve problems together, which is the core of a good partnership. I found the later books in that series explored their teamwork better than the early ones.