yes your waiting period ("karensperiode") starts the day from when you are approved for dagpenge as graduate in your A-kasse. Graduates with a waiting period are not required to register at the Jobcenter (Jobnet.dk) before the month has passed. If they do this anyway, they will be called in for talks with the A-kasse and the Jobcenter.
So if that date will be the 19th of December then your quarantine period will be gone 1 month later (19th of January 2020).
After that you will have right to receive dagpenge, but you dont need to. If you still want more holiday, you can just tell the A-kasse/Jobcenter that you are on holiday and don't want to receive dagpenge. Remember always to notify Jobcenter/A-kasse about holiday at latest 14 days before start of holiday.
On your monthly "dagpengekort" for January 2020, you must register that you have been on holiday from 19th of January to 1st of February. Then you will not receive dagpenge for your holiday, from 19th of January to 1st of February.
When you come back to Denmark, around 1st of February, you must register as unemployed in Jobcenter (Jobnet.dk). The A-kasse will then pay you dagpenge from 1st of February, because from that date you no longer have waiting period or holiday, and therefore are fully available for the labor market.