Domino.js comes with both a tree builder as well as a DOM library. RemexHtml covers the tree builder piece and is in use in various Wikimedia codebases. It currently integrates with the PHP-DOM-libxml combo which we would need to replace with the new DOM library.
So, this task is to figure out the details involved in the integration with RemexHtml, write the code for it, and test it. This may necessitate adding configuration options in RemexHtml if it doesn't already exist to pick a DOM library (see T271728: Migration strategy from DOMDocument to Dodo).