In English to ask "Is that your own XXX" is a question meaning did you produce it. Is that your own bread? Is that your own painting? Is that your own child? I have never met a person that has produced a dog so the question should translate as "Is that your dog?"
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Related to your comment, do you perhaps have a reference for your statement that it can only apply to something you produced yourself. The dictionary indicates that own is: "Used with a possessive to emphasize that someone or something belongs or relates to the person mentioned". Which indicates that it does not have to mean that the dog in this case was produced by someone.
Other than that, these sentences do not have to refer to "humans", as you might remember the sentence Zijn grootvader is een schaap.
Indeed! I guess I never thought it would be directed to a dog. Thank you.
As usual, context would help... Imagine someone who usually walks other people's dogs, and you find him/her going out from his/her house with a dog... You could ask him... «Is that your own dog?», and it would make a lot of sense, I think.
I don't know it if would work similarly in Dutch...