Honestly, when it comes to more in-depth BDSM questions, I tend to point people over to @instructor144 because in my opinion, he is the end all and be all of advice in D/s relationships and far more knowledgeable than I am. I have no problem recognizing that and I’d rather be thoughtful with your intimacy than feed you some lame response to something I don’t really know firsthand.
That being said, collaring means different things to different people; if pet play is involved then it is different than how I have personally dealt with it, hence my reluctance to provide a complete answer to your question.
In my experience with collars, it’s been just another bondage toy similar to cuffs, nipple clamps, rope, Hitachi, and a blindfold. It’s hot to slap a collar on a woman and incorporate the leash, hold her by it during sex and foreplay, and pull her to you when having sex, but I don’t personally desire to walk her around the room like a pet, but I would never say there is anything wrong with somebody who does enjoy that. Pet play is just not a turn on for me.
I would definitely ask your dom, before you do it, or anything, “what it means to him”. Maybe he sees it like me, in which case it’s not really that big of a deal. It’s less scary than cuffs, in my opinion. But if it invites a new type of kink, you should communicate beforehand so that you are comfortable with it.
Hope that was helpful.