Canonically, dogs do not have souls. But I rather suspect that since He is in “every things”, they might have one, yes. As Cats and Roses might, too. Uncanonically speaking (ahem) that is.
As to my “wonderings”, well, pretty simple:
“I cannot at the moment” …. “I will remain silent on that” …. “on a very tight leash”
Food enough for “wondering”, wouldn’t your PostPositivist, Kantian mind, also think ?
But what the hell, maybe it’s just me and my lack of True Knowledge.
Your move, pal.