[Rachael x]

I reputable breeder does not cross breed dogs.
Yorkies and Poodles are both classed as hypoallergenic, but that does not mean that you wont get a reaction from them.
I am allergic to both dog saliva and fur, Poppy (yorkie) does not bring me out in a reaction at all but my schnauzer cross does. But my aunt has asthma and dog allergies and both my yorkie and my schnauzer give her a reaction. So not everyone is the same.
I recommend you find a reputable breeder of either yorkies or poodles, ask if you and your family are able to visit them and spend some time with her dogs to see how your allergies are around them before purchasing a dog which you may not be able to keep.