Absolutely! In my opinion, as a personal trainer and business owner you should have liability and any other insurance related to running your business BEFORE you start training. Without full coverage related to your business – no matter where you are training clients (e.g. their home, your own home, outdoors etc), you expose yourself and your personal effects at risk from a lawsuit related to your work.
There are many places where you can find information on liability and other insurance for your personal training business (e.g. IDEA’s website, your certifying organization etc.). What I would recommend is that when you contact an insurance agent that you talk to them directly and explain EXACTLY what you intend to do with your practice and training so that they can best advise you on what type, and how much insurance coverage would suit you.
Good luck and I hope that this helps.