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Add the option
Together with the other options.
Julian was on the right track as to why you are not seeing the period, but the answer will not give you want you want. When you do a dataexport you have to think of it like any grid retrieval where you have to have something in the rows and something in the columns. Therefore if you have 12 dimensions, you will have 11 members in the row and columns for the 12th value. In your case since you fix on a single period, you are getting that period as a column value. Unfortunately Dataexport does not display the names of the columns. Were you to fix on Jan:Dec, you would have 12 columns , one for each period. The columns are always a dense dimension that dataexport will pick unless you explicitly specify what dimension is the columns (as Julian described).
The only way I Know to get what you want is to add an additional dense dimension to the cube with a single member then you can use that for the dense dimension and get the periods in the rows. If you can't do that to your existing cube, you could create a clone of the cube, add the dimension, export the data from your cube into the new cube and then run your dataexport from there
Thank you both.