LARISA, you are the spouse of an EEA citizen exercising, or intending to exercise, their EEA/EU Treaty Rights in the UK. Those rights include the ability to be employed, or indeed self-employed.
As their Family Member you have the same EEA/EU Treaty Rights. As you will see from your EEA Family Permit it is for just 6 months. Once you are in the UK, and it would be best if you make the application after you have started work, rather than before, you need to apply on form EEA2 for a Residence Card. That will be valid for 5 years.