Are you REALLY exporting.... or are you using the AE Render Queue or Adobe Media Encoder for the task?
And does this animated graphic require an alpha channel?
It would help if we knew your render settings, your experience level with AE, a little more about your workflow. Even knowing what version of AE and what OS may be helpful. This is probably just user error. Normal workflow would be to add the composition to the render cue, select a folder (the desktop is a lousy place to store assets by the way) and then press render. Without changing anything you'll get lossless DIm (digital intermediate) suitable for use in any NLE but not suitable for playback. If you need transparency then you should select lossless with alpha in the output module from the pull down.
If you want something else then tell us more.
Inside AE, if you see a search help field at the top right corner of the app type in 'rendering,' press enter, then read through the first two articles.