I'm not 100% sure (never tried it with a RobotNanny), but typically pets are fine by themselves for a few hours. I once played a single sim with two dogs, and they did just fine when he went to work. Maybe it would be different if they had puppies, but adult animals can be left on their own provided they have food, toys, etc.
As for the RobotNanny, it's not fully automated unless you have autonomy turned on in the options. In fact, I was a bit bummed out about this when I first found this out. From a programming standpoint, Plumbots are regular sims with some features/ interactions added and some taken away. This means that your NannyBot will (theoretically) be better at tending to the needs of babies better than a non-Nanny plumbot, but pets have very different needs.
Note: Unless they fixed this in patch .67, DO NOT EVER LEAVE A NANNYBOT IN CHARGE OF AN INFANT. When Futures first released, I made a single woman who built herself an army of bots. One cleaned, two had corporate jobs, one was a politician, and one was a full-time nanny. I turned autonomy up to high except for my controlled sim, and let the plumbots run free, expecting they would take care of the house.
WorkerBot1 and WorkerBot2 worked perfectly; they would charge themselves at home, stand around when not at work, and then skyrocketed through the ranks, raking in the cash.
PoliticianBot worked fine (provided my sim threw the parties) UNTIL I rewarded him with a sentience chip for reaching the top of the career... at which point he sat around all day in the hottub, missing work, not campaigning, not getting paid, and generally being a nuissance. (There's a joke in there about a mindless robot making a better Leader of the Free World.)
MaidBot only cleaned half the house. It was a very large mansion with an open space between the "living" area and the "sleeping" area... essentially two houses connected only by a skybridge and a basement. She never crossed into the sleeping area unless I specifically directed her to a task over there (eg, making a bed); however, even if there were three beds to make, she would immediately go back to the living area after making only one bed. So I never had dirty dishes or messes in the living area, but the sleeping area was a wreck.
NannyBot was a complete disaster from LITERALLY the second the baby came home; she was pillow fighting when the mother came home at 5am with a screaming newborn and passed out in the entryway from exhaustion. Over the next several real-life hours, I tried easily two dozen different configurations of trait chips, room layouts, and structural accommodations. Eventually, the ONLY two traits NannyBot had were RoboNanny and Efficiency, because with any other combination of trait chips she would get distracted and ignore the baby. The only pieces of furniture in the nursery were the crib and a plumbot charging station because with ANY other piece of furniture (including baby toys) she would get distracted and ignore the baby. The only door leading out was open to everyone in the household except Nannybot, because she would leave the room and ignore the baby. I had to remove my "Wire House with Speakers" because she would dance and ignore the baby. Eventually I had to remove all of the windows from the room because she would stare out the windows and ignore the baby.
So that's what I ended up doing: locked her and the baby in a windowless, soundless, objectless gray box... and NannyBot literally stood next to the crib just watching while the baby starved to death.
I wouldn't trust my pet fish to a RoboNanny, but I don't think it will matter for your dogs provided you leave them some food.
