Being a German myself, I would say that it doesn't matter ;) A PhD from Denmark will be probably even higher regarded as you did something a little bit outstanding and not the usual Bachelor at Uni A, Master at Uni A, PhD at Uni A (assuming of course you perform as well as you would in Germany).
Maybe you'll get something like "chris077, PhD" instead of "Dr. chris077". It will be definitely no disadvantage in terms of jobs. Every employer will see in CV and cover letter that you did your PhD.
I disagree a bit with the statement that doctor titles have some value and advantages in Germany. It used to be like that but nowadays you impress some senior citizens...at best. You can pave the streets with Dr.'s in Germany, so don't let that be the reason to not pursue a PhD in another country ;)
I think it is a good decision. Usually you get 4 years of funding with a reasonable salary in Denmark. Good luck with your application!