No problem
Yes when I said residence card I meant GNIB card (GNIB cards the residence cards issued by Ireland, and what they allow the holder to do - work/study/or none depends on the Stamp number that is stated on the card).
The final Stamp 4 EUFam and temporary Stamp 4 I mentioned come with GNIB cards (both for the temporary one and the final one, once they have made a decision they will send you a letter asking you to goto the GNIB office, where they will put a stamp on your wife's passport along with the date until which she is allowed to stay in Ireland, and also issue her a GNIB card which states her stamp type and is what she should carry with her as an ID and what she would use for things like proving that she is allowed to work here). So once she has these cards there is no need for additional registration (the only potential issue is that between the time it takes for you to find a job and for them to issue the temporary card, the initial 3 months period could run out).
As long as as your employment is documented and you have a proper contract and are paying taxes/PRSI, you can do any job including part-time and it will make no difference for the EU1 application - if you are legally working and can prove your relationship they have to approve her application. You can also be self employed, but then they will ask for proofs that you have your own business (bank account with regular cash inflow from customers and/or paperwork related to your company).
Lastly, my advice would be for you to have a look at the application form and the required documentation before you come to Ireland. Some documents depend on your employment and other on your accommodation, and to avoid any delay it would be a good thing to know exactly what you need and make sure it would not be an issue with your future employer and landlord before you sign any contract with them.