Please provide more information of your system including :
RAM, Graphics Card, Processor, Disk Storage, Third party Plugins used (if any, for eg- VideoCopilot's,etc.)
Check out the blog on this issue by Todd : solutions for problems with QuickTime files in After Effects CC (12.0) because of conflict with DVCPROHDVideoOutput Quic…
And follow troubleshooting steps as mentioned.
What kind of Quicktime? If you are trying to use the h.264 Quicktime then you are doomed from the start because it never worked well and Apple is not developing or improving that container any more. If it's some other format then you may have other installation issues. I would never deliver a Quicktime h.264 to anyone because of the problems with the format. An MP4 container for h.264 is universal and dependable. Use the AME to produce that.
If you need another Quicktime format we need to know the details before any advice other than check your version, make sure that you don't have any 3rd party codec packs installed and make sure your system and AE is up to date will only be a wild guess.