Gearboxes are normally pretty hardy units. I am guessing that the only way it would make a noise in just one gear is if the gear teeth are worn. Try draining the oil and see if loads of swarf comes out as well. if it doesnt and you cant feel any undue vibration then I wouldnt worry about it. I am the worlds worst at worrying about strange noises when all that is needed is a pair of ear plugs........
Best to just go till it goes man, if it is the box it will go anyway, but those things are freakin solid!
Do you want to spend the time and money just to find out it's not the issue? Mine sounds like piston slapping in high revs but I dont give a toss (should really get breakdown tbh)
DT uses a straight cut gearbox, pretty much like the reverse gear on a car which does whine, what it could be is one of a few things, may be your oil that needs topping up/draining, could be that the gear is worn and not sitting on the shaft properly (would probably knock) and worst of all it could be that the bearing is on its way out, if it is that the bearing is on its way out or the gear is worn then that is not a good thing, reason that you might only be hearing it in 6th is because the gearbox is under heavier load which would put heavier load on the bearing, if it was knocking then I would say that a tooth had cracked but you really need to keep an eye on it as a bearing in your gearbox failing will not be a good thing, if it gets any worse then I would definitly strip it and see about picking up a new gear depending on if the gear has any more play that the other gears or is damaged, otherwise I would replace the bearings. How many miles has your bike done since new and since last oil change?
Sounds like it could be one of the other things then, by the way, which oil did you use, I put a thinner oil in my gearbox the first time I changed mine and it felt a lot different, the gearbox more precise and mechanical, like you could feel every tooth on every gear but it also made more noise, when I took the motor to bits there was no wear on the gears or anything either so a thinner oil is just fine. what have you put in? 10w 40 or 10w 30 or what?