Margaret Peacock, 64, from Farnborough, avoided jail after she stuffed the border collie puppies in a freezer and beat another to death with a tin opener.
Peacock feared the puppies might have genetic mutations because their parents had been sister and brother.
She appeared at Basingstoke Magistrates' Court on March 2 when magistrate Dr Susan Dadlani said her previous good record of keeping animals meant they would not be disqualifying her from continuing to do so, despite what she had done.
But a petition was started following the incident, calling Peacock to be banned from owning and breeding any pets for the rest of her life.
It has been signed by more than 25,000 people.
Now, The Kennel Club, which operates the national register of pedigree dogs in the UK and acts as a lobby group on issues involving dogs, has said it has suspended Peacock's registration activity pending its own investigation.
A spokesperson from the Kennel Club said: “The Kennel Club takes any cases of animal cruelty extremely seriously.
"Mrs Peacock's registration activity is suspended pending our internal investigations. She last registered puppies with the Kennel Club in 2015, prior to her being sentenced.
“The Kennel Club does not have the power in law to prevent people from owning/keeping animals – such power lies with the courts.”
But it looks unlikely that Peacock will be banned from owning animals, as the petition requests.
Her Majesty’s Courts and Tribunal Service don’t comment on sentences, but a spokesperson told Get Hampshire : " If members of the public are unhappy with a sentence in the crown court they can ask the Attorney General to consider it under the Unduly Lenient Sentence scheme.
"This though does not extend to magistrate court sentences."
An RSPCA spokesperson said: "This was clearly a very upsetting case and one in which we are pleased that the court convicted the defendant of animal cruelty offences following the prosecution case brought by the RSPCA.
“The sentence imposed was a matter for the court to decide and we respect that decision."