First, you have to understand the investment. An annuity is a contract between you and your insurance company. You make a lump-sum payment or series of payments. In return, the insurer agrees to make periodic payments to you beginning immediately or at some future date. Annuities typically offer tax-deferred growth of earnings.
Is this a fixed annuity or a variable annuity? A fixed annuity pays a fixed interest rate, while variable annuities are invested in a range of investment options that are typically mutual funds.
Is it an immediate annuity where you start receiving income payments right away, or is it a deferred annuity where you're investing now and will start receiving the annuity payments at some point in the future? Are you planning/hoping to go back to work, or does this mark the start of your retirement?
Social Security acts as a fixed annuity that has an inflation rider for retirees who qualify for it. Taking Social Security prior to your full retirement age reduces your monthly retirement benefits. You could be better off using the money in your IRA to fund living expenses up until your full retirement age of 66 or until you find work.
A $10,000 purchase of an annuity isn't going to materially change your income stream in retirement. If you used it to buy an immediate annuity today, it would provide you with a lifetime monthly income of about $54. Invest in a deferred variable annuity, and that investment may grow over time and potentially provide you with a higher monthly income stream when you eventually decide to begin receiving payments.
Investing in a deferred variable annuity within an IRA account is usually a bad idea. You don't need the annuity's tax-deferral feature because you already have the tax deferral within the IRA. Taking a taxable distribution from the IRA to buy the deferred variable annuity isn't likely to make tax sense either because the distribution will be taxable income.
I'd suggest keeping your powder dry and not buy this annuity while you're unemployed and uncertain about your prospects.