Hi Sarah,
You will need 2xphoto id...eg. passport & drivers licence or passport and long version of birth certificate. You will need proof of address e.g. a recent utility bill/bank statement or tenancy agreement (in your case you are renting so your tenancy agreement or if there is a utility bill in your name for the rented property). Ideally a P45 or a letter from your employer stating that your employment has been terminated. Did you receive a redundancy package and if so you will need to bring your RP50 that you should have received from your employer. Did you receive an ex gratia redundancy payment as well as statutary redundancy... if you received an ex gratia payment and the total redundancy package is over €50,000 there will be a disqualification period depending on the amount of the package over €50,000. Hope this is of some help. If you need any other info please feel free to pm me.