Existence of Deuterium peroxide
It does exist. At least Google shows one supplier situated in New Jersey.


  ID 1130   Deuterium Peroxide (30% in D2O) D2O2    98  5   5.0g / 10.0g


Though for some reason I could not find any reputable supplier like Cambridge Isotopes or Sigma-Aldrich (strange!). As far as physical properties are concerned, as pointed out by @snurden there exists a significant amount of literature. Here is one article from the Canadian Journal of Chemistry that includes study of many properties (behind a pay wall though).

Abstract:



And to answer final part of your question: