Nick here from Shopify.
It would definitely be possible to buy a new domain and link it to your store. You can have up to 10 different domain names on your store on any plan at one time, but you can only choose one primary domain.
I'm wondering if you can renew the same domain with GoDaddy though so you might not have to change domains? Unless you want to change it that is. But yes, if you change the domain, everything will work the same as before, but you will simply have a new domain name.
Shopify has a help guide going into more detail about your domain which you might find useful here. Let me know if you have any other questions about this!
All the best, Nick