Actually, I've found it pretty easy to keep a down bag dry. Of course I grew up with the things--in 1941 when I went on my first backpack (age 6), there weren't any synthetic sleeping bags (the only synthetic fabric around then was rayon). Keep it inside a watertight bag and unload it only under your shelter. Air the bag out whenever you get a dry hour or two. Don't wear wet clothing inside it. Either use a tent that's well-ventilated and avoid camping in low-lying areas to avoid tent condensation (whether the tent is single-wall or double-wall), or wipe down the walls of the tent during the night and before you move around. (Of course if you have a dog, he may be up and doing the whole body tail-wag first.) Under a tarp, use a bivy with a fully breathable top (to avoid condensation) to protect the bag from blown-in rain or snow. In below freezing temperatures, use a vapor barrier to avoid your body moisture's condensing on the inside of the shell. Having a DWR (but highly breathable) coating on the shell helps.

From my own experience, I can tell you that a wet synthetic bag is just as cold as a wet down bag. Synthetic insulation is easier to dry, because it doesn't tend to clump as down does, but the "warm when wet" myth that synthetic bag proponents claim is strictly folklore. I've been there, done that, and it ain't true! Whatever your insulation, be sure to keep your sleeping bag dry!

EDIT: I would never get a down bag for a 6-year-old, though, unless (s)he has progressed several years beyond the bed-wetting stage! I have no idea how my parents coped with that little problem!