Ok, I have tried this a few different ways and am now thoroughly stuck. I am trying to get an NPC intro to kick the stage of my quest forwards when they say it. Now if that dialogue were part of my quest it would be easy, but its no and I am struggling.

I have tried to create a property for my quest but its not working so I have clearly done something wrong. Could someone help out here? I'm trying to use this to learn the scripting in Skyrim but so far its like banging my head against a wall.

Well, what should work is:
Create a property in the dialogue fragment - assign the other quest to this property
Then you should be able to reference the quest from the dialogue script.

Alternatively, you can have the dialogue do a SetStage() on its quest, and then that STAGE will reference a QUEST property.