I would be very cautious at the job, if your supervisor or who ever is over you "thinks" your issues are/ can/ will interfere with your work performance you can loose your job.
However, you can speak to who ever is in charge and say your dog is having issues right now and would it be ok if you took him with you or your dog needs meds during the day and it would be easier to give if he was with you rather then leaving the job to go home. A little white lie will not send you to hell
. As long as the dog is well behaved, no barking, no messing on the floor they could say ok.
Two of the privately owned companies I worked for in NY allowed us to bring our dogs to work, I had rascals, barking, Diva girls, I never took them to work, besides I had 3, I would have to had taken the gang