NO! The Dog Lovers Registration is for dogs of any ancestry, you just pay your money and they give you 'papers' - unfortunately with so many KC reg staffs about, you will find it extremely difficult to find buyers for the puppies - apart from which, how would you know if the dog you use is her brother or even her father? (Not quite sure if its your bitch that is not registered or the dog you want to use? - If its your bitch then find a KC reg dog)
Please reconsider - there are way too many
Staffs being bred, and if you want another one, why not rescue one instead of adding to the overpopulation. Also so many people want Staffs for the wrong reasons - to make them look macho for instance. If you are thinking of breeding just to make money, think again, so much can go wrong and you could end up losing your bitch and having a huge vets bill, as Staff often have to have caesarians due to the size of the heads.
Also Staffs suffer from two major hereditary diseases for which there are DNA tests, L2-HGA and Hereditary Cataracts - You would be hard pushed to find a reputable breeder who would let their dog mate your bitch if she is not tested for these.