There is a formula I used to use when accepting contractual work like that so I will simplify it so that you can get an idea of how to proceed. Let's assume a full time job is willing to pay you $60,000.00 on a quarterly basis, you're earning $15,000.00 Let's assume the average amount of time you will be without a job, you will be losing that $15,000.00
For starters we have $75,000.00 to work with in which you should go not go under. Now, you would be literally making a parallel move from full time with benefits to contractual work. If you bought your own insurance with yourself +1 (spouse/kid) you're looking at about 6k per year. Which means, $75,000.00 - 6,600.00 you'd come away with. You're contract work at the $75,000 per year mark comes to about $68,400.00 if you did this parallel move. This translates to about 32.88 per hour per 40 hour work week per 260 workdays.
So you have one rate: 32.88 (new contract rate) versus your normal salary of $60k which is 28.84 per hour. A mere 14% raise in which on the worse case, will cost you more if you go three months dark after your contract is up.
Me... I wouldn't go under $45.00 per hour (93,600) per year which gives me 6 months of downtime when the contract is up. Of which, $45.00 is sort of insulting, I've had people offer me $75p/h for 6 months worth of work. Might sound like a lot, but its 78,000 at 6 months. You need to remember, contracts are not guaranteed, so you need to set a threshold and do the math according to your expenses and tack on between 3-6 months of downtime when work is non-existent.
You will also need to set aside your own taxes, SS, etc., however at that point, you'd be surprised what you can write off. Do like General Electric does... Everything is a loss.