Pet Safety and Protection Act of 2019 This bill revises requirements concerning the sources of dogs and cats used by research facilities. Specifically, the bill revises the list of permissible sources of dogs and cats used by research facilities to include dogs and cats obtained (1) from a licensed dealer, (2) from a publicly owned and operated pound or shelter that meets specified requirements, (3) by donation from a person who bred and raised the dog or cat or owned it for not less than one year, or (4) from a research facility licensed by the Department of Agriculture. The requirements pertaining to sources apply to dogs and cats obtained through sales, donations, or offers. Monetary penalties are established for violations.