Connecting a domain

Hi

I need to connect my client's existing/old site, which has a domain in a different name to the new one I have built in Squarespace, in order to do the 301 page redirects. When I connect to the existing site, held with 1&1, will that affect the new site on Squarespace in any way? We want to go live with the new SQS site tomorrow but I haven't done the connection & page redirects yet, because the existing site needs to remain live & active. Once you start a domain connection for this purpose, can the new Squarespace site still be switched on while the connection is happening in the background? And when I input the 301's, can the site remain live while I do that?

Thank you!

Perhaps, I am not understanding the question...if your SS site has a different domain name assigned to it, why would redirecting the old domain name to the new one now work and why would both sites not be live? Please rephrase the question.