this is also covered in the answer of another question: http://a-kasser.dk/qa/332/is-it-too-late-to-join-a-kasse.
It is correct that you as an EU-citizen can transfer your rights concerning contribution and working-periods.
BUT this require of you that you apply for membership of an danish A-kasse within 8 weeks after you ceased to be insured in another EU country. And further there is the requirement that you within the 8 weeks must begin work in Denmark of at least 296 hours over 12 weeks / 3 months. The last requirement does not apply to Nordic nationals, who within the last 5 years have been entitled to Unemployment benefits in Denmark, or have received Unemployment benefits.
Since you came here in mid july it seems for us that you are too late.
What we know about the 8-weeks rule is that it is taken strict. But at the same time we want to inform you that we don't know all regulation in detail. We dont think so, but maybe it is possible that A-kasse will make exemption - try to contact an A-kasse of your choice as quick as possible.
Best regards and good luck with this..