Mary,
First, welcome to our forum! I'm an EMT-Basic, so I can only comment on what I've seen in the field, and heard from my partners.
The Paramedic program is extremely mentally and physically challenging. I truly believe that any person that has a passion for EMS can pass the academic portion of the class. It's going to take dedication for a year, but it can be done!
As far as the physical part of EMS, that is also demanding. I'm a 6'2" pretty regular build guy. My partner is probably 5'0" tall. Neither of us are really built for EMS, and there are times where we've had to call for a lift-assist. Here is what I can offer you:
1. Work on upper body strength. When I first started working, on my first day, I didn't realize how heavy the stretcher (90 lbs) with Pt, O2, and LifePak12 were. In fact I was having problems lifting the stretcher's wheels off the ground so they could lock. Work on the upper body!
2. Find a system! When you first get a partner in EMS, work out a system. Being the tell guy, I was always at the pt's head. I often had shorter partners, so they would lift the patient in two stages. If we had a heavy patient going home from the hospital, we'd raise the hospital bed to the height of our stretcher, instead of lowering the stretcher, and having to raise it again. Find your own system, it will make things a lot easier!
3. Stay fit - In EMS you will continually place strain on your body through the normal course of your shift. In private EMS, I sit in an ambulance for 12 hours, and go home and sleep the day away, only to wake up and do it again. It's critical that you stay fit, eat health, and exercise. Besides reducing injuries, it will keep you on top of your game.
4. Never be too proud - You must realize your limitations. I believe that anyone in EMS should be able to lift a 250 lb. pt on a stretcher with a partner. That's about 300 lbs between two people, including the stretcher and equipment. The reality of this is much different than my expectations though. If you can't safely lift a patient, tell your partner. You can always call for a lift-assist, meaning another unit will come and help out. Don't hesitate to ask police and firefighters for help, they like to do that type of stuff.
I understand a lof of my advice was related to the field, and not an agility test, but that's all I can really offer. Besides a physical and other medical tests, I was never tested for my strength or agility. I think if private companies started testing, you would notice a sharp decline in the amount of applicants.
I hope this is somewhat helpful, and once again welcome to our forum!