There's no way to tell it exactly I think, I just waited for a few weeks and when my Pet(s) were still nominated then I assumed they were entered in the queue. ^^;
After your Pet gets rejected it is banned from being nominated again for a short period of time so if you check the profile daily you'll notice when the "Pet has been nominated..." is suddenly gone. I guess that's what these people do, stalking their own Pets so to say. =D