Embedding suggests uploading to a video website like Vimeo, YouTube, etc.
Such sites take nearly any video and churn out various resolution streams for playback on their site / embedded / full screen / etc.
Vimeo for example scales videos to 720p (should remain 720x720 for your 1:1 aspect video file) unless you are 'plus' user which allows 1080p.
To be as much in charge of this kind of conversion as you can be, it pays to prepare the video yourself into the format the site likes best. Again for Vimeo they have compression guidelines published to assist with this:
http://vimeo.com/help/compressionHope this helps,
niels