If you apply for Unemployment benefits ("dagpenge") between 17th October-31th December 2019, you will meet the requirement of stay in Denmark for at least 5 out of the last 12 years.
And you will also meet the requirement of at least 1 year membership of A-kasse.
I assume you also fulfill the income-requirement saying that you must have earned at least DKK 233,376 during the last 3 years (in you case since you entered A-kasse, because only periods with A-kasse membership can be included in the income).
This income-requirement must be fulfilled on the day you apply for benefits (October 2019).
So, you should be able to get Unemployment benefits if you don't find job after your current contract ends.