Considering the fact that the 1st of Muharram is not a national holiday either I doubt January 1st will be declared a holiday anytime soon. Cos when they do then many will demand the same for the 1st of Muharram as well since after all the Islamic new year begins on that day and Qatar being Muslim country, will then be expected to give that day off as well.
Personally we don't celebrate either day but will not refuse an extra holiday be it 1st or 31st!