There's several ways to look at this...
If Disney does a good job of maintaining its brand, promoting its characters, and creating new characters, they have absolutely nothing to worry about. However, their record in this is a bit spotty, and I think there is room for others to steal some thunder away.
However, I'd hardly call Nickelodeon the "New Disney". Spongebob is doing great right now, and Nickelodeon has done a good job of coming up with new characters that the kiddies like every few years.
But they have yet to create anything that rivals the Disney characters for longevity, or even the Loonytoons for that matter.
Rugrats are the next Peanuts? Please.
Now, I'm not saying Nickelodeon hasn't been succesful, or that they can't grow in the future. But SO FAR, they have not found a way to connect with adults the way Disney did, and even the way Looneytoons did.
As for Mickey Mouse, kids of the 70's didn't have Mickey Mouse on the brain either, so I wouldn't be too concerned about him for that reason. But he has become a "corporate symbol" as Robin Williams said, so his popularity could eventually be hurt if Disney continues to allow their brand power to diminish.
As is usually the case, if Disney just concerns itself with what Disney does, and does it RIGHT, they will be fine.