As long as Tiffy is fit (not overweight), and you warm up pleanty before every class then I would recomend it. It's real good mental stimulation and it's great excersise. Tiffy may have to be a little older to enroll in class, check with your nearest agility school to see what age requirements they have.

As for her back, just be careful and use your own good judgement. Doxy's are very prone to back problems as you know, so start slow and only do what the instructor advises. I have heard horror stories of slightly overweight dogs going right from sleeping on the couch, to the car, and then to agility class, where they tore a cruciate ligiment on their first jump due to lack of warming up and streching muscles before a run. As long as you make sure she has streched her muscles, she can do agilty just fine.