You will be out a job in 4 months because that is what contract coding is. During periods of heavy coding need - now- you will be working as much as you need. If you said you would work 40 hours make sure that you do that because contract companies are very picky with that.
If it were me, I would continue searching for a job, but work this one so you are getting paid and gaining experience. This job is doing HCC Coding which is using ICD-9 codes. Make sure to get all the details on how many records you are required to complete per hour, what the error percent will be because that is very important as well.
Some companies provide you a computer to work on the system so make sure you ask that as well. Did you fill out W-2 forms? If so, then you are not working as a 1099 coder, and you will be paid with taxes taken out. If you did not fill out any W-2 forms (State or Federal) then you are a 1099 employee and you will need to claim at the end of the year.
Good luck to you. Hope I helped with some of your questions.