White fungus is usually a result of harmless bacteria leeching out of the wood, and the fungus is a type of algae that grows and eats the bacteria, which is common in tanks and on various driftwoods (especially ones that were submerged, dried out, then submerged again- which may of happened prior to you getting it).. I sometimes get it. Go ahead and if it's on the driftwood branch to take the branch out and rinse it off in hot water. It usually tends to go away on it's own after a few weeks.
Or it could be slime mold.. they both grow in tanks, on woods.. below are two pictures, one of each.. do either resemble what you have?
If the first one then it is what I mentioned above and can be cleaned off easily and will come back most likely, eventually it will go away. (The picture is an extreme case of it, and of not being cleaned off)
If it's the second picture it is plasmodial slime mold- and treatment is basically the same thing. They actually feed on bacteria and the bacteria is feeding off of excess organic waste in the gravel. Slime molds are not harmful to your fish but fish usually don't like it.
After you clean it, your tank cycled and you bring your fish in, make sure not to over feed, or allow food to fall to the bottom- usually feed the pellets one at a time (2-3 per feeding, twice a day) to make sure none are being ignored.. if the fish doesn't eat, remove the pellets within minutes. That will not allow the mold to have more food source.