There's no proof of a home release (especially this early) for Unikitty. If there was a release, the following is likely to happen, based on other modern show releases I've seen:
DVD may be a smaller market nowadays and therefore less likely to be the format chosen. Blu-Ray maybe but many people realize digital and streaming are the norm, so through mediums like iTunes (which is established and growing for Unikitty) the show would gain attention.And this is coming from a guy who would like to have a DVD copy of the show too eventually. January 10 is barely enough time to let the episodes breathe on cable and online before home release. Barely enough episodes for a proper Season 1 release or even an in-between release as some shows like Spongebob occassionally do.
A standard tv show contains 20+ episodes for a season: Spongebob Season 9 had 26 and OK KO is still in its first season with 43. If anything we're at a thirdway point, and even if the episodes air online fast, they are behind on cable premieres (usually 2 days behind), I wouldn't expect the season to be done so soon. Episodes premiere about a week apart and I'm sure some will have reruns in between to keep momentum and avoid large hiatuses.