After having problems with damping off when potting up germinated veg seedlings, toms, peppers etc.. I was advised to use vermiculite on the surface of the compost ensuring there is ample around the stems, and water the new plants from below. I seldom lose a plant to damping off now whether that be flowers or veg when potting up for the first time.
If a plant needs potting up a second time I add perlite to the compost mix, this helps retain moisture so the pot doesn't need to be watered as much.