One question on the 'Duchy of Cornwall'; as this is the fiefdom of the Prince of Wales, are you figuring him in as the ruler?
Also, with a population of just over half a million how do you propose to fund such a defence force?
Yes, the Duke of Cornwall would be Head of State of the Duchy of Cornwall whilst also being Prince of Wales and heir to the throne in the UK and the Commonwealth Realms. He would have similar powers and role as the Queen in the UK, in mainly a ceremonial role with government carried out by the Cornish Assembly.
Initially, clearly Cornwall could not afford such a force. However, I would expect the EU to provide some financial support, maybe with aircraft leased to begin with. The UK may also give some support with the transition of airspace and territorial waters to Cornwall, with the Royal Navy also paying to keep RNAS Culdrose open for them to continue to use.
Just for comparison, according to wiki:
Malta - pop: 453,000 and 13 aircraft
Montenegro - pop: 625,000 and 23 active aircraft
Cornish pasties, because they cannot be made anywhere else.
EDIT: And tin and possibly lead/arsenic.
Definitely Cornish pasties. That's all they'll need, the whole world will be buying them by the container load
Maybe some Cornish ice cream too - it is the best in the world after all.
I suppose they could reopen some of the tin mines, and increase capacity at the china clay pits. Fishing and farming would also be important exports as well as a large income from tourism. I won't go for the easy option and say they find oil...