Squarespace

I have a live website on Squarespace (www.ladybrooknursery.com). I have created a new website design in Squarespace and need the domain transferring to the new design, so that I can make that site live, and take down the old one. In addition any SEO/redirects of old pages to new to retain link authority would be helpful. The website is small - only 5 or 6 pages.