I can't think of anything that would be an 'obvious' sign that you were having sex with the dog - depending on the dog, there will be some slight behavioral changes but nothing that would be an indication that you are fucking her. Physical changes in the vagina would only really be noticeable right after the act but otherwise nothing that would draw any attention.
If anything, it might be your own behavior around the dog that might suggest somethings up, but as long as you're not "doing the deed" in the next room or anything, it shouldn't be something anyone is going to notice.
Even with small changes that you might be worried about, the majority of people are not going to have "He's fucking the dog" as their first thought - just exercise some caution and restraint, and you won't have a problem