Dear Nelly Overcomer,
A marriage conducted in Denmark is legally valid in Germany if the spouses fulfil the conditions for marriage according to their respective right of origin and the marriage has been entered into in a formally effective manner according to Danish law. In Germany there is no legal obligation to register such a marriage. However, it makes sense to have the marriage certificate authenticated by the Danish Ministry of Foreign Affairs.
Whether or not you can apply for a residence permit for family reunion to your wife in Germany, depends on the citizenship of your wife. Only if she is EU-citizen and enjoy the right to free movement (e.g. when she is employee with at least 10 working hours per week) in Germany, you can apply for the residence card (Aufenthaltskarte) at the Immigration Authority at the place of your stay in Germany. If your wife is German or Non EU-citizen, you have to leave Germany and apply for the visa for Family reunion in the German embassy in Italy or in your home Country.