Yes. it is a good idea.
Below is the recommendation from ACSMs Resources for the Group Exercise Instructors.
This segment of the manual was authored by Shirley Archer, JD,MA
“In today’s litigious environment, for the most protection, a GEI should carry professional liability insurance ($2 million per occurrence is the recommended amount), even when working in a business as an employee, where the GEI may be covered under the business owner’s policy. The reason for this is that it is not unusual for a single claim to result in a million-dollar judgment. Purchasing the best protection enables you to perform your job responsibly and to feel confident your career will not be destroyed by one mishap. Most insurers of GEIs provide coverage for certified professionals.”
You can purchase insurance through IDEA.
Editor, ACSMs Resources for the Group Exercise Instructor
I would recommend it. The reason is that somebody may ask you for personal training outside of the facility, and your will have to have your own insurance then.
The rates for the professional liability insurance may vary by insurance company. When I carried my own insurance before I had a studio, the rate was about $200 per year (this is from the year 2001, though.)