Hello there. I am sorry you are worried about your beardie. As previous posters have mentioned, even though you wanted brumation explained fully, we need to consider environmental issues as well. I think where you are you should be able to get the Arcadia TUBE bulb. Please don't get the coil bulb
And although 14 months old they can brumate, if I am not mistaking it is still Summer where you are? But with a cough, I am more worried about an Upper Respiratory infection (URI). The vets, if thats what they have, will give you an antibiotic to fight the infection. Too much humidity can cause the URI's. i hope you understand that people are trying to help you by asking all the questions that seem unrelated to brumation, but the bearded dragon's environment should be looked at first and foremost.
The article they have on here is great for it as well.
and yes I speak from experience dont get Desert 50 bulbs either