What if everyone needs their dog's gender identifying?
In my opinion, the thing to remember is what our goal is on Pets Stack Exchange. We're trying to build a repository of question and answers that can serve users for many years to follow. The questions we ask here need to be comparatively useful to current and future readers. Questions that work best are more general than the one you've posted because current or future readers are unlikely to be concerned about the specific gender of one dog.
I know the subject matter of the question itself could be seen as somewhat controversial considering the backstory of the dog...
The backstory feels somewhat irrelevant to me because, again, the real question it seems like you want to be asking is 'How can I tell the gender of a dog?'. This means that users who arrive with the same question don't have to ask specifically about their dog too they can just apply the general rules without asking another question.
If everyone posted a picture of a dog and asked the gender we end up with hundreds of images (which aren't accessible for users with vision impairments) all asking effectively the same question.
Is it Primarily Opinion Based?
I agree with @JAD here, it may not be completely opinion based, and I would have been tempted to close as 'Too Broad', but it's not a question that brings value to the site.
You are entirely welcome to ask the question of 'How can I tell the gender of a dog?' because then we teach our users how to identify the gender of a dog rather than giving them the answer to one specific case.