My dog is more likely to bark at noises or smells during the night when he's sleeping on the ground under a tarp or in his dog hammock. In a tent he's cut off from the outside enough that he's likely to be quieter. I've seen posts from others that had the same reactions from their dogs, but dogs are individuals. YMMV. At Trail Days in Damascus last year my dog voiced grave concerns about late night revelers. In popular areas like Dolly Sods, WV, I try to camp several hundred feet off of trails and away from regularly used campsites. This has seemed to work, but then he may just be growing up.
This points out the biggest issue with camping with dogs. Every dog is different and unlike people they can't tell you what they would preffer. So you need to take your dog out on overnighters to see what works for them and how they act. I wouldn't commit to a gear purchase for the dog until you know how they preffer to sleep. If you spend a lot of money on a small tent, and they are like my dog then you wasted the money. Same for if you buy them their own tarp and they want to be enclosed.