I use Amazon a lot. For me, they usually ship orders out the same day or the next, but I have an Amazon Prime account which is sort of "enhanced" so they do things faster. For normal orders, I'd say expect them to ship your order out two days after you place it, and allow one to two weeks for delivery via USPS (free shipping, usually). Other shipping methods, like UPS or especially FedEx, will deliver your package faster.
But I think if you order now you certainly have time.
(Alternatives would be to purchase your music digitally, via the iTunes Music Store, or Amazon has a rather large selection of MP3 albums as well, where you instantly download the music after purchase.)