If you move in with your partner, you are no longer entitled to OFP whether you start work or not.
If you don't move in and start work, you can earn up to 146 euro pw without affecting your OFP. Anything over that will start to reduce your OFP, and if you earn over 425 euro pw, your OFP will stop. Your Rent Supplement may be affected as well.
Entitlement to Rent Supplement as a family will depend on circumstances - what income you and/or your partner is on. If either of you are working full-time, you can't qualify for Rent Supplement.