Hi,
no there should be no problems for you to use the 3 months jobserach rule.
You are already approved for unemployment benefits based on your education from University (graduate rule), so you do not need to be a member for 1 year.
So you have the same rights to use the 3 months jobserach rule as others on unemployment beneifts.
Therefore you must also meet the same requirements for using the 3 months rule. You can read about the requirements here: https://www.a-kasser.dk/transferring-unemployment-benefits/
You do not need to keep your address in Denmark, while you are looking for job in another EU-country.
And yes, you need to apply for a PD U2 form from your A-kasse.
Best regards,
Anders Weber, www.a-kasser.dk