Correct — the DreamHost "mirror" option only works with domains that are already hosted here. It's basically just a way to make one domain that we host use all the same settings as another one.
I'm afraid it's not actually possible to cleanly "transfer" a site from SquareSpace — they retain copyright to the layout, so you'll have to redesign the site to host it here. (All part of their cunning business plan, I suppose!) The XML file probably contains the text of your posts, but it's likely to be in a proprietary format. Worst case, you may have to manually copy and paste your posts out of the file (by opening the XML file in a text editor) to get them out.