Yup not a flea, it's some kind of small beetle. If you think you have fleas in the house, put a shallow bowl/kitchen dish filled with warm water and a little bit of dish soap on the floor in the room you suspect, in this case wherever the dog sleeps would be a good idea. shut the room and leave it for an hour or so. If there are any fleas they will be attracted to the heat jump in and then not be able to get out and you will see them.
What's brown and sticky? ... a stick. Or a tiny ad.