Using 'the' in front of proper nouns?

This may be an incredibly stupid question but I'm having a bit of trouble with it.

If I want to write:

I transferred flights at the airport.

Then I know I need to use 'at the' as 'airport' is a noun.

but what if I want to specify the airport to be Sydney Domestic Airport?

I'm of (the perhaps wrong?) belief that 'Sydney Domestic Airport' is a proper noun and so you shouldn't need the preceding 'the'? But reading it out loud either way seems correct.

So what fundamental rule am I obviously forgetting from primary school? Go easy on me!