If you want the IR to be useable in EASAland on an EASA aeroplane, you need an EASA IR - which is a lot of theoretical knowledge study before you can do the flying course.
If you're thinking of going to FAAland to do it, then I'd have thought that you want to get a standalone FAA PPL first, then you can properly add an FAA IR to it.
A third option is that here in the UK we have a UK-only IR(R) [Instrument Rating (Restricted)] - which is highly regarded here, but only useable in Britain. I suspect that you can't add it to a Danish issued PPL EASA PPL either, but no harm in asking the Danish authority how they'd feel about that, as it's cheaper, less theoretical study - but at least gives you a valuable skillset, useable at home in an emergency, and you could just pop over to the UK every 2 years to renew it.
G