I've recently got a 13 Cooper hardtop w/o the armrest.
As far as I know, there are no items on the market that says the item will fit 2013 model.
Would this
http://www.ebay.com/itm/MINI-Cooper-...=mtr#vi-ilComp
fit my baby?
If not, can someone recommend me one? (oem preferred.)

 

The oem armrest fits just fine. My '13 did not have one when I looked at it but they installed one "free" before I drove it off the lot.

I think a lot of parts are still listed as only working up to the '12 just because the '13s are so new

 

I have that armrest and like it. Go for it.