Johanna,
I think you'd be better off with getting an adult dog who is already used to life with cats. Yes, people who work full time jobs are allowed to have dogs. However, I don't think being alone for 10 hours is the right situation for a puppy.

They need to be socialized, potty trained (even if it was in a litter box,) played with, fed 3 times a day, etc. Raising a puppy IS like a full time job. It's almost like raising a child.

Granted, an adult dog may have problems with being left alone too. Many dogs have seperation anxiety that will need to be trained. Of course, doggie daycare, if available, is always an option as well.