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Being that you will be on Interstate highways for a vast majority of the trip, it's not going to be desolate. You should be looking at I-5 to CA-46 to CA-99 to CA-58 to I-40. Plan on taking 4 days for the trip, which will be about 500 miles and 8 to 10 hours per day. You shouldn't have a problem finding pet-friendly hotels. Plan on frequent rest stops to exercise both you and your dog.