Fraser is clearly a first class source but could still be wrong. Yet it does suggest some other information being available on the subject.
I think his comment came from his nearly 50 years working and running Davidson. He may remember Davidson making dogs or alternatively remembers being told they were made in the 1880s. Also as Adam pointed out Dog could just be refering to a Victorian glass oddity.
Davidson did make a lion ornament, this is documented in the Pricing Committee records, so they could have made a dog ornament as well. But unless some documentary evidence is available, we can only say they may have been made by Davidson.
The Claude Fraser booklet also contains a typo which has been copied by many people in articles and web pages. He got the dates of the Davidson fire wrong, suggesting they factory was closed for over a year, when in fact it was closed for just 3 months.