To add query fragment just put it inside the option array:

    $node->content['links']['add_bookin_unit_link'] = array(
        '#weight' => 10,
        '#theme' => 'link',
        '#path' => 'node/add/er-engagement',
        '#text' => t('Add attendee data'),
        '#options' => array(
            'html' => FALSE,
            'query' => array('field_er_cal_entity_reference' => $node->nid)
        ),
    );

This will return an URL like this: node/add/er-engagement?field_er_cal_entity_reference=13