I would definitely get certified. If you wish to get into this type of training, a certification other than your Physical Therapist will be required.
Is there any specific type of clients or population which you are looking to work with (athletes, kids, seniors, groups, 1-on-1, etc.)? This will help you narrow down the type of certifications you need to be focusing at. There are many great certifications which offer continuing education and other perks that will help you improve your knowledge as a fitness trainer. ACE, NSCA, ACSM offer some high level certifications.
Also keep in mind that you will need liability insurance as well. You can find one here in IDEA at https://www.ideafit.com/fitness-insurance .
I hope this helps.