She formally became queen of Denmark in 1533, but due to the Civil War (Count's Feud) that immediately followed her husband's accession to the throne, her coronation did not take place until 1537.
She was repeatedly pointed out by contemporaries to have been politically active and to have participated in state affairs, but these comments are only general statements and do not describe exactly how and within which issues she took an interest and used her influence.
As the first lady of the royal household, queen Dorothea hosted festivities with great splendor when motivated as representation of royal power, but was in everyday life described as strict, moral and frugal; she supervised the finances of the household herself, allowed for no waste and had all members of the court in constant occupation, allowing her ladies-in-waiting no time for leisure.
Her intended marriage, however, was opposed by various theologians who considered it impossible for a widow to marry her late husband's brother and was eventually prevented, despite several years efforts from Dorothea's part to bring it about.
In parallel, Dorothea successfully opposed her son the king's desired marriage with her maid of honor Anne Hardenberg, a matter which was also drawn out for years.
[1] Dorothea considered it her God given right and duty as a mother not only to love but to advise and rule over her children, including her son the king, and once wrote: However, Frederick II detested both her reprimands and her attempts to involve in state affairs as she had done during his father's reign.
Her son Frederick II greatly disliked her interference and warned her to stay out of state affairs in no uncertain terms, upon which she replied: "We can, God be praised, do without this long journey to Sweden and now have a good day with a clear conscience [...] You may be convinced, that we have no intention to trouble ourselves in this matter, when we can understand from your letter that you now better" - but she resumed her efforts to act as a mediator the following year.
[1] She defended herself by saying that she had only intended to benefit Denmark, but the king suspected her for treason and had her informally exiled to Sønderborg Castle, where she resided the remainder of her life.