Is it really possible to be a vegetarian paleo?

I began eating meat about 7 months ago.  Prior to that I hadn't eaten a
stitch of anything that was once alive for 13 years.  During those 13 years,
I was constantly subject to Epstein Barr, Mononucleosis, Chronic Fatigue,
Strep Throat (on a regular basis), viral bronchitis:  basically I spent most
of my time sick.

For the past months which i have been a paleo, I (knock on wood) have not had
so much as the common cold.

My point?  I guess it would be that, while I can agree with vegetarianism
from a moral point of view (which is why I was unable to consume animal
flesh), but from a health standpoint, it is clearly not such a good thing.

Besides, as a paleo-vegetarian, where would you ever manage to get enough
protein (and fat)?