Actually, you might have more of a problem under trademark law than copyright.
"Disney" is considered a very strong trademark because its so recognizable and famous. Even with a disclaimer saying you aren't affiliated with the Disney company, you could still face a trademark dilution claim if you use "disney" in the domain name.
In all likelihood, Disney isn't going to sue you at the outset. You'll get a cease-and-desist letter first. As long as you cease using whatever they aren't happy about, they'll probably be satisfied.