Cockett has built a distinguished career in sheep genomics research, maintaining an active research program even while serving in various leadership positions at USU. Her research program has centered on the identification of genetic markers associated with economically important traits in sheep, as well as the development of resources that advance research on the sheep genome. Cockett and her colleagues published an article describing the sheep genome sequence in Science in 2014. Her current project focuses on the identification of genetic regions associated with entropion in newborn lambs. Cockett has served as the United States coordinator for sheep genome mapping since 1993 and is an active member of the International Sheep Genomics Consortium.

As an active researcher, Cockett has received many awards and accolades throughout her career including a Young Scientist Award from the Western Section of the American Society of Animal Science (ASAS), the Utah Governor's Medal for Science and Technology (2004 and 2015) and one of USU’s top honors, the D. Wynne Thorne Research Award.

Since beginning her tenure as president, Cockett has prioritized diversity and inclusion throughout the USU campus system. She was instrumental in creating the Latinx Cultural Center, developing and hosting an annual Inclusive Excellence Symposium, investing in the USU Inclusion Center, creating the Center for Intersectional Gender Studies and Research, and facilitating a new community-campus partnership in the annual Community Diversity Dinner.