A Maltese poodle is a small, cute, white, curly, fluffy dog. It is a friendly pet and is small enough to carry. Maltese poodles are good natured, and make great pets.
So why can't one find a breeder?
The reason is, they are not considered a "breed." So there are no official "breeders."
They cannot be registered. No one keeps pedigrees (family trees.) Because the family trees are not in writing, the dogs cannot be said to be "pedigreed."
If two people who own little white dogs agree to let their dogs mate, then more little white dogs will ensue. Some puppies may differ in size or colour from the litter mates. This is caused by a recessive gene emerging from an unknown ancestor. Which puppy is the right size? No one can say, because there is no breed standard in writing. Some folk like miniature Maltese poodles, others like bigger Maltese poodles.
Maybe some day, Maltese poodle fanciers will get together and discuss what size the dogs should be. They will write down, "No higher than ... cms..." Then they will decide on the colour, "Must not be all black," (for example) In this way, a "Breed Standard" will be established. Folk whose dogs are in line with the breed standard, will start keeping records of which dog mates with whom.
So eventually, we may have registered Maltese poodles, but in the meantime, if you are looking for Maltese poodle puppies, just keep looking in the newspapers and vets' notice boards.