quickOSM uses the Overpass API. you can also use http://overpass-turbo.eu/ to access the Overpass API without QGIS. i’ve only looked into OSM / Overpass for this particular discussion, but it looks like Overpass needs to return nodes to get coordinates. so you have to use some advanced scripting to get the nodes associated with the relation (or something like that). in this case, i think you can run this script:
<osm-script>
<id-query ref="1773407" type="relation"/>
<recurse into="x" type="node-relation"/>
<union>
<item/>
<recurse type="down"/>
</union>
<print mode="meta"/>
</osm-script>
or
<osm-script>
<union into="_">
<id-query ref="1773407" type="relation"/>
<recurse into="x" type="node-relation"/>
<recurse type="node-way"/>
<recurse type="way-relation"/>
</union>
<union into="_">
<item set="_"/>
<recurse type="relation-way"/>
</union>
<union into="_">
<item set="_"/>
<recurse into="x" type="relation-node"/>
<recurse type="way-node"/>
</union>
<print mode="meta"/>
</osm-script>
then export the resulting polygon as kml.
here’s a language guide for the Overpass API: https://wiki.openstreetmap.org/wiki/Overpass_API/Language_Guide
here’s what it looks like when i run the query above from overpass turbo: