I have a logo type of design in Illustrator that I want to use to create an one-inch sticker. The sticker is used as a branding product label that one would stick on a gift-basket or evelope to close it shut, etc.

What online place can I upload the design and then they can print me some stickers that they would postal mail to me?

Here's an on-line company that has a 3 day turn around and here are file preparation tips from that site.

Here's the Google search link where I found it. There are a lot of companies that can provide the services you need. Take a few moments to go through each site and get a few on-line quotes. Make the best decision based on what meets your needs as well as your budget.