If you're not a current customer here, then be sure that you sign up for full price. I think if you pay for one year, they'll waive the setup fee and you'll pay $9.95 x 12, whatever that is. Remember that you can't use a promo code if you want the hosting transferred over to you.
Make sure that the current developer is ready to ask DreamHost Support to transfer the domain's hosting (and registration) over to you. Once you're confident the developer will follow through, pay for the hosting here and then have the developer contact Support to move the site over to you.
Once that's done, you might have to iron out a few kinks, so post back if you have more questions or need other help.