I am not sure what you mean by saying: "was my application on A-kasser.dk enough?".
We, www.a-kasser.dk are not an A-kasse ourself. But we have on our website links to sign up forms for all 24 A-kasser.
So if you mean that you have signed up for instance through a link from our website and received confimation email from the A-kasse, then you have done enough.
But you have not signed up to any A-kasse, just by register as a user at our Q&A-forum on www.a-kasser.dk, or by using our contactform.
If you have signed up for an A-kasse, you can always change to another A-kasse later, and your membership periods will be transfered to/calculated by the new A-kasse.
So please check your confirmation email you received 10 months ago, and be sure that it is an email from an A-kasse (and not A-kasser.dk), confirming that you have become a member.