A month?! Sometimes the crew working on DS9 and Enterprise had less than two weeks to get sets, props, and costumes together. I'm much more concerned about the short shrift given to the 50th anniversary special than to this.
Adjusted for inflation, it probably did. Fifteen years ago, DS9's budget was in the $1.4 million range per an episode. Even eight years ago, when the Eccleston season was airing, Battlestar Galactica cost $1.6 million an episode. Doctor Who's budget is in the £1.0 million range per episode. On a similar note, I wouldn't be at all surprised if Elementary spends more on one 45 minute episode than Sherlock spends on one 90 minute episode.
I've done some 3-D animation before. The main problems that would be caused in post-production due to having two images would be the effects shots. Aside from the fact that they would have to be rendered twice, when they interact with live-action, they have to be perfectly aligned or else the 3-D won't work. I've also looked at some 3-D TVs and the cheaper, passive ones worked so much better than the very expensive shutter ones. The shutter glasses caused eyestrain and made everything but the TV flicker. And the picture looked rather flat as well.