As of 2015, in the state of Illinois you had to complete your postdoc in its entirety to be eligible to sit for the EPPP. Consequently, I know many people in Illinois who have decided to sit for other state's exams (Kansas being a popular choice).
If time is of the essence, I would not recommend applying for the exam in Illinois.
Edited to add: I just saw that you are on a two year postdoc. The requirement in Illinois to sit for the exam is one year of internship and one year of postdoctoral work. If you will get all of your clinical contact hours in your first year of post doc you may be able to apply to take the Illinois exam after you have completed 1 year. However, it's important to note that many 2-year postdocs don't have enough clinical contact hours for you to be able to do this.
Good luck!