Thank you for posting! It's not possible to purchase private registration through us for a domain registered elsewhere. In order to transfer your domain, you need to remove private registration. Unfortunately, if the registrar you want to transfer to doesn't offer private registration, you'll need to have your information be listed in the Whois Database. One option to consider is to keep your domain registered here and just point it to your hosting.
Hi @amykholt. Thanks for being part of GoDaddy Community! If you have whois privacy through GoDaddy and you want to remove it to transfer elsewhere, you would need to cancel the Private Registration service. Hope that helps.