@peter H5N1 is notable for infecting a wide variety of mammalian species including dogs and dogs have already been documented to have died from it. You also have recent studies suggesting cross-infection between owners and their pets.
There's also a strain of H5N1, the D1.1 sub-strain, which has been more associated with severe human infections than the strain widely seen in dairy cows in cattle. The D1.1 strain appears to have made the jump to cows in New Mexico in the last few months.