Welcome to the Wefugees Community and thank you for reaching out to us as well as for your nice words! :-)
Yes, many people get married in Denmark as it seems to be comparatively easy and it is also recognized in Germany (as far as I know).
However, I doubt that the marriage in Denmark will save you from the family reunification visa process. Even couples who get married in Germany are requested to obtain a visa from a German embassy for the subsequent residence permit according to section 28 of the German Residence Act. I will link my colleague dear @mbeon-Éanna here to correct me in case.
Unfortunately, the visa procedure can take some time. Is there any chance to extend your residence permit in Hungary for the time being?
I recommend you to contact a migration counselling office for support. In Berlin there are many organizations offering free of charge and expert advice. Please use this search engine to find a respective office.
I hope this helps and all the best,