When you live (again) in Denmark, you can always become member of an danish A-kasse, regardless of you are employed or unemployed.
However, if you want to transfer your earned rights (working periods and insurance periods) from another EU/EEA country's Unemployment Insurance Scheme to the danish A-kasse, the requirements differ depending on whether you have been member of a danish A-kasse within the last 5 years or not.
In your case, where you have been member within the last 5 years (actually within the last few months) you can have your rights from the Czech republic transfered to the danish A-kasse. The only requirement you need to fullfill is that you must get a PD U1 document from the unemployment insurance office in Czech republic (see below).
For instance you dont need to work here in Denmark before you can have your rights transfered, and in this way you can get Unemployment benefits ("dagpenge") if you (still) meet the requirements for being eligible for dagpenge.
You don't tell us if you in june (after graduation) had your graduate rights registered in "Min A-kasse". Thats very important concerning your possibility to being eligible for Unemployment benefits after returning to Denmark. Because you only have been member for few months in Min A-kasse before leaving Denmark, then it is not relevant to ask if you have been working in Denmark and by this way could have earned right to benefits. Because only work/income earned during membership periods in an A-kasse counts to meet the "income-requirement" for being eligible for dagpenge.
Your only chance to get benefits will therefore be if you have had your graduate rights registered in the A-kasse at latest 14 days after graduation in June 2018.
Transfer earned rights from Czech republic Unemloyment Insurance Scheme:
Now that you are member of the Unemployment insurance system in Czech republic...you tell you are..I assume this is the public recognized Unemployment Insurance in Czech republic. If thats the case, then you must ask the Unemployment Insurance office in Czech republic about a "PD U1" document. This is a document that is used when moving between Insurance systems within EU-countries. The PD U1 document includes information about how long you have been member and working periods.
With a PD U1 document you can transfer your earned rights (membership period and working period) to the danish A-kasse.
You must do it within 8 weeks after canceling insurance in Czech republic. However we strongly recommend to rejoin the A-kasse right after returning to Denmark.
When you say you don't know about this PD U1 document I assume that you did not get your earned rights from the danish A-kasse transfered to the insurance in Czech republic when you moved there. I am not sure whether this will have consequences for your rights now when you want to reenter the danish A-kasse.
You must ask Min A-kasse, how they will see your case regarding earned rights. But this "problem" is actually only important if you had your graduate rights registered in Min A-klasse in June.
If you did not do that, then you will probably only have the rights earned in Czech republic...employment of 2 months.
If this will be the case for you then you need to work at least 10 months here in Denmark, before you can get Unemployment benefits.
So it is a little difficult to answer precisely what your situation is, because we don't know your full member story in Min A-kasse.
If you need a more precise answer you must tell us whether you are registered with graduate rights in Min A-kasse, and whether you had your rights transfered to the Czech republic system when you moved there.
Please post any comments in this Q&A-forum.
Anders Weber, www.a-kasser.dk