My average is about 4-5 days (total playing time) for one character. That said if you just went from planet to planet, complete every quest and have an easy time finding groups for heroics you could do it much quicker I'd suspect.
Space missions are great for a boost (as tedious as they may be), particularly between levels 15-20.
Warzones can also slow you down quite a bit depending on your system spec's (Load times in and out of Wz's can kill your progress rate, more so if your on a large planet, e.g. Belsavis).
Just my 2 cents
EDIT:
Forgot to note that the above total playing time is without skipping any conversation dialogue. If your interested in the story you could cut your time down quite a bit.