that should be fine unless your water is really bad. The only problem with brita filters is that they don't get everything. Even filtered brita water will leave white watermarks on all your glass. I recommend buying spring water or using RO. If you are using brita water, keep as much of it off glass as possible.
I use aged (at least 48hrs) brita water for both my misting and raising tads. I do not have any trouble (or water marks), but I must say that I live in a city with excellent drinking water. I heard they going to pass a "Brightwater" act which would put flouride in the tap water, I'll have to see if the Brita can filter that out. When keeping eggs moist, I just buy a gallon of drinking water at the store and add two drops of Mythylene Blue. I have never had a problem.
I'm from the east bay area of california and use britta only for water bowls in the snake room. i use RO or distilled - depending on the application, but nothing else. Britta will leave water marks and if you read the fine print, there are still things that get through in my area.