edited to add: Duh....just realized I'm answering a thread that is waaaaaaaaaay old!
Here's the scoop:
California has agricultural inspection at major highways: traveller pulls into a lane, like a toll booth on an expressway. The bored attendent asks, "Do you have any plants, fruits, vegetables or animals?" and traveller says, "Yes, I have my dogs Fido and Fifi, and apples that I bought at Safeway in Reno" and is waved on.
If, on the other hand, the traveller says "I have my pet goat, Capricorn, and peaches from my Uncle Willy's pesticide-free organic farm in Cougar, Oregon" she will probably be asked for Capricorn's health certificate, and may need to toss the peaches.
They're looking for anything that might harm California's agricultural industry. There are occasions, for example, when, due to mayfly infestations, ALL apples are banned from importation.
Border Patrol inspections are totally different. They don't care about fruit and pets.
It's always good to carry a copy of your dog's rabies certificate, as well as copies of receipts for kennel cough, DAL2PP, etc. Some state and county parks, in states where rabies is a problem, require that pets have proof of rabies vaccination.
Finally, FYI, Dawg and I drive between Raleigh and Austin regularly: 1,350-ish miles. Fastest route, if you can avoid hitting Atlanta at rush hour, is on 79 from Round Rock/Taylor to Shreveport, then across I-20 to Atlanta, then up I-85. If you are likely to hit Atlanta at rush hour, hook north on I-59 at Birmingham to Chattanooga and then up to I-40. This is about 50 miles longer, but may be faster.
Meridian, MS is about the halfway point (650 miles from Austin, 700 miles to RDU.) La Quinta and Motel 6 (exit 253 on Hwy 20) accept pets.