No. The address supplied by your builder is enough for a link, invitation or QR code. A custom domain can be easier to say or print, but it adds a renewal responsibility. Choose a short spelling that both families can type. Avoid changing the address after invitations go out unless you have checked how the old link will behave.
Buying a domain and connecting one are different actions. Buying registers the address; connecting points an address you already own to your wedding website. Forwarding sends visitors onward to a different address and is not the same as hosting the site at your domain. Ask which behavior your builder supports.