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

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

$node->content['links']['extra_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