A K1 is authorised to work for 90 days on entry. The problem is proving it. One way is to get the temporary stamp at JFK, as has been suggested. This might not be practical for you. You can file for K-1 classification EAD, but most people don't bother - by the time it's processed, it's usually got only a few days left to run.
The best chance you have of working instantly and as close to instantly as possible is to fly in through JFK and get stamped, get married and file for AOS and EAD ASAP (like, within two days), adn then if the regular AOS classification hasn't arrived, file for interim EAD 90 days after submitting your AOS application.
Be aware that you do have to stop working between the expiry of the K1 EAD and the receipt of the AOS 1-year one; because they are different classifications, it doesn't count as a renewal.
Hope that makes sense...!