A mother carrying her four-month-old baby watched in horror as police doused her family's beloved pet dog Daisy in capsicum spray and then shot her dead.

Daisy had become tangled in her leash causing her to fight with the family's other dog Princess but, before Kirsten Small could intervene, plainclothes police killed the Staffy Cross.

The 32-year-old mother was carrying baby Eva in a sling on her front and the pair was covered by the capsicum spray aimed at Daisy, leaving Small fearing for her daughter's safety.

Daisy's playmate Bugsy was also with her on a leash and, like Small, was still traumatized yesterday by the shooting outside her Ermington home last Thursday.

"They shot my dog three times in front of me. They were judge, jury and executioner and it is just not right," Small said.

"I didn't know they were police, they were plainclothes, they just stopped and I was saying I needed a stick and they sprayed stuff and I was asking what are you spraying and my baby was screaming.

"She got it all over her baby carrier, it missed her eyes. I keep seeing the gun, I keep playing it back in my head.

Police confirmed senior police were investigating the incident but declined to comment further.

Two-year-old Daisy had grown up playing with Shitzus, Chihuahuas and other small dogs without incident and Small said she had also been protective of Eva in her pram.

Small's father Mick was outraged at the shooting.

"They're called Daisy and Princess, that gives you an idea of how wild they are," Mr. Small said. "It is overkill - literally."

Daisy's ashes were returned to the family this week after her body was taken to the RSPCA.

RSPCA Inspector Skye Adams confirmed she was called to see Princess and to assess her for injuries.

"There are no charges being considered with regards to the police or the owner in relation to the prevention of animal cruelty acts," she said.