No. Unless you are so distracted that they can prosecute you under the generic "endangering aircraft/passengers" rules. But there are no specific rules about filming in/from an aircraft. (Except in the Netherlands, where the government never cancelled the cold-war-era legislation on this.)
Having said that, the distraction part is a real issue. If you can mount, turn on and then forget the camera: fine. In all other cases I would urge you to abandon the whole project and simply wait until you're allowed to carry passengers, and ask them to do the filming for you.