I used to carry a dog with me - and she really was my "co-pilot". Just about everything One and two4theroad said is true, however. While my truck was in the shop, I spent many a long day sitting outside with her at terminals and truckstops.
You have to carry extra bottled water with you (I speak from experience that refilling a jug from a truckstop or rest area is NOT a good idea). You have to carry food. Training is a BIG issue - they need to be completely housebroken and you have to be willing to make more stops. I was lucky, my girl usually only needed to stop about twice a day. Truck damage is an issue - if you have a nervous or bored dog, they WILL chew on things. I was lucky to avoid that, but my company truck showed signs from a previous driver's animal... and even if they don't chew, shedding is an issue for a longer haired breed. You need to be willing to clean your truck every few days. I even carried a handheld Bissell machine for my carpeting when I was longhaul.
Some customers will also not allow a dog to be present in the cab while you are being loaded/unloaded. There was a few times I had to close the curtains on mine and tell her to hush so that she would not be found - thankfully she listened.
Also, another truckstop hazard that was not really mentioned.... other drivers. I have had another driver on several occassions attempt to run my dog over with his truck - not that she ran in front of him, but a deliberate attempt on the driver's part. Beware.