The first suggestion:

Distance de Chicago en Australie

is wrong, it translates to "Distance of Chicago, Australia"

the second one:

Distance de Chicago à l’Australie

is technically correct but sounds odd. I would only use it between two similar entities:

Distance de Chicago à New-York

Distance de la Terre à la Lune

The issue is the form de … à somewhat convey the idea the distance between both locations depend on which direction it is measured. As it is usually not the case, I would prefer to use the more symmetrical entre … et which is usable between whatever entities:

Distance entre Chicago et l’Australie.

Distance entre les États-Unis et l’Australie.

Distance entre Chicago et Sidney

Distance entre la Terre et le Soleil