From my personal experience it will take you roughly 7-10 Months for a Blue Belt. I believe that is the only belt that you can get in the alloted time frame. Everything else would depend on what Ironman said to the T, even the Blue Belt.
I train under Hermes Franca and Kurt Pellegrino and I am hoping to be a Brown Belt in about 5 years. It's not set in stone, just something for me personally to work towards.
Also, does your gym offer No-Gi as well? Try to even go to those classes so you can get more mat time in. Nothing better than more practice.