to use the special graduate rule you should have signed up for A-kasse at latest 2 weeks after graduation - so unfortunately you can not use that special graduate rule anymore.
You will only be able to get unemployment benefits after 1 year membership, and only if you in that period earn enough to meet the income-requirement. You must have earned/have had an income of at least DKK 233,376 (in 2019) during the next year, if you want to be eligible for unemployment benefits after 1 year membership.
You don't tell us if you are an EU-citizen or not. However we assume that you are an EU-citizen and therefore meet the residence requirement, which is an additional requirement for being eligible for unemployment benefits.
Anders Weber, www.a-kasser.dk