Eventually the 1099-G information will be in the Wage and Income Transcript from the IRS, but it probably won't be there until June or July. You could file an extension and wait for it to show up in the Wage and Income Transcript. A drawback of the IRS transcript is that it does not show the state tax withheld, but for Florida that's not a problem.
If you do file an extension, remember that it's only an extension of time to file the tax return, not an extension of time to pay any tax due. You should estimate the tax as best you can, and if it looks like there will be a payment due on the tax return, make a payment before April 18 to reduce or eliminate any possible penalty for late payment.
