Not Anon - of course you should aim for what the market will bear. I didn't disagree with Mr Cool but as with all these helpful tips to a newcomer, no-one actually gives the OP an actual figure to guide him/her so still leaving them in the dark.
The point I was making is as a starting point a guaranteed 12 months work to start you off as a contractor is not a bad intro to this world and at an effective 20K pay rise too which I happen to think is quite a good position to be in before you establish yourself and demand higher rates.
OP - assuming you are not a world famous guru at something then you seem to have lined up a nice opening into the world of contracting. As a guide I started low as no-one knew me (not being world famous myself!) and have nearly doubled my rates in 2 years of doing this so it doesn't have to be a slow process to increase your rates - as long as you remain good value for money and keep delivering what is asked of you then you will keep getting work.
Mr Cool - you may be on higher rates hence the "hardly worth getting out of bed for" comment but your circumstances may be different, certainly I assume you have the benefit of experience at this, and the OP does appear to have a good opportunity presented to them - and who is to say the OP won't overtake all of our day rates in the future...
...provided they get on the contracting ladder at some point of course!