It is strongly advised to settle your taxes with SKAT (the national tax office) before you go abroad.
In the following links you will get an overview of how you are generally covered when you go abroad as a non-Danish citizen. Please note that these are very general rules, and you should always contact your local tax centre to enquire about your personal tax situation.
The most important things to look into are:
If you are leaving Denmark, it is important to clarify your tax situation before going abroad. You can find important information from the Danish Tax Authorities here:
AU has a special agreement with PWC on advice packages in connection with in- and expatriation. Read the overvies of prices and services (pdf)
Read more about taxation for expatriates in this guide from KPMG. The guide is in Danish.