Not sure if you figured this out. I’ve been trying to figure this out for a bit as it has forced my students to use QuickPost in the Dashboard of their sites.
I changed
if ( property_exists( $wp_query, 'query' ) && array_key_exists( 'page_id', $wp_query->query ) ) {
to
if ( property_exists( $wp_query, 'query' ) && array_key_exists( 'page_id', $wp_query ) ) {
I think it works now as the error is no longer showing up. I also noted that this only happens in IE, not in Chrome.