We travelled in Dec 12 from eastern Long Island to TV with our 4 yr old beagle. We stopped in Fredericksburg and then next day drove to Port Wentworth,(Savannah area) Georgia. Hampton Inn as mentioned above was great, and no pet fee.
We left at about seven am and sailed on 195 even though it was a weekday.
95 to Ormond Beach, then 40 West to 19 South and to Marion County Road 42 into TV on Belle Meade up by Mulberry and bear right onto Buena Vista and straight on to Village of Hemingway.
Best wishes for a safe trip with your little one