Britton here with the Shopify support team.
If you have multiple domains and want to set up a 301 redirect from one to another it would need to be done under online store > domains. You would need to set one of our domains as a primary domain and then click the "redirect all traffic to this domain" button. The resulting redirection is a 301 redirect.
You can find full instructions in our documentation.
I hope that helps!
Britton's answer should do it Joni. I've done it for over 10 client stores. If that doesn't work, you may have something wrong with your cname or A record setup (have only seen this problem once).