Don't let your female see you watching her when she is digging or she will likely abandon the hole. If she does it often enough it can lead to eggbinding. You can feed and water her when she is back up in her branches. Be aware that a female may dig several test holes before chosing the one she wants to lay the eggs in when not being watched. She does this to select a site that she considers suitable.
Once she has laid the eggs, let her bury them completely and return to the branches before you dig them up. Dig them up carefully and when moving them to the container you are going to incubate them in try not to rotate/turn them. Its a good idea to have the incubator and container that you are going to put the eggs in set up ahead of time.
I incubate them at about 78F. They are not in a closed in incubator so the temperature fluctuates a bit at...lower at night. (My incubator consists of a people's heating pad with a wooden frame (rectangle) that I have put screen over. I raise it to the height that puts the temperature in the container at 78F by using shims under the wooden frame. I have used this method for over 15 years and had good hatch rates not only with several species of chameleon, but also water dragons, several species of geckos, coneheads, three-toed box turtles and quite a few other reptiles. (The temperature has to be adjusted for some species by raising or lowering the frame.)
I use the coarse type of vermiculite, barely damp. I use shoe-box sized tupperware-type containers with two very very tiny holes in the lid. I fill these containers about half full of the slightly damp vermiculite and lay the eggs in rows in them in slight indentations that I make with my thumb. By only filling the containers half full there is "head room" for the babies when they hatch until they can be discovered and removed from the container.
By placing the eggs an inch apart in all directions the eggs will hatch almost individually. In my experience, it seems to produce a better survival rate.
Good luck!
(You are lucky to have a vet that makes house calls!)