The MQL property wildcard (*) can only be applied to one type so you'll need to individually list the properties that you want to see like this:
[{
"type": "/event/disaster",
"/time/event/start_date": null,
"*": null,
"limit": 10
}]
Another way to do this would be to use the Search API to specify which property values to return (by type or domain) like this:
?filter=(all type:/event/disaster)
&output=(all:/event/disaster all:/time/event)