Hello and welcome to the RTA forums !

With your set up and just wanting to get across country I would suggest sticking to the Interstates, checking the weather forecasts/road conditions before setting out to see if one route would be more favourable over another. (I-40 or I-10/20 for example) It's possible to do the trip in 5 days, but it'll be long days behind the wheel, day after day. Personally I would allow 6, and keep one in reserve in case of any weather related delays. With decent rest/lunch stops and to let the dog stretch out and run around, it would work out to 8 to 9 hour days on the road. You can normally find Motels with drive through type parking close to the Interstate, and where possible stop on the East side of any major city so that you will be heading away from the morning rush and not into it.