Before you send your passport for a residence card, you can give yourself a couple of months to look for a suitable job.
The "Family Permit" sticker in the passport, states that you will be allowed to work, show that to any prospective employer and it will be ok.
Even after your passport is sent to the Immigration service, you will be covered by their reply letter of receipt, as it will say that you are allowed to work or/and start a business.
After a while of being married, I would suggest you try to obtain also Hungarian nationality without giving up your own, as this will make it much easier to visit other Schengen area countries.
Next year my wife will be entitled to Italian dual nationality, which will be just a little more than a formality.