Danish Facebook users have for some time now exchanged information and helped others find old friends, family or just an old school mate, and you too can join this group AND others!
.....(click the header to read more)
First of course you do need to be on Facebook, but then all you need to get started look for the Facebook group:
"Søg efter den du ikke har set i mange år"
Being a Danish group you likely will have best results if you post in Danish.

Over the time I have been following the group we have had a few looking for Danes here in Australia, and some with good results.
But mostly it is old school friends or or play mates from childhood.
To have the best prospects of success you post as much information as possible, name, age and year and locations or as much as you have.

Maybe more relevant to Danes here in Australia, several FB groups cater to the local Danes.

The Danish Club Official meeting point / Group

The Danish Club Newstead Page

Dansk i Brisbane/Queensland Group

Heimdal Brisbane Page

Heimdal Brisbane Families w/kids Group

Danish Club in Brisbane
Danskere Fastboende I Australien & New Zealand

Danish Club and Danes in Brisbane History
Dobbelt Statsborgerskab