The fawn won't be far, maybe 25 yards unless the doe was spooked and that's the reason she ran into the road.
Fawns are pre programmed for two thngs "sit" and "Run"
You won't know which it will do. Start looking in knee high brush and near logs etc where it can lay motionless yet still have an avenue for escape.
Think like a deer, where yould you leave your baby while you search for food?
Best thing would have been to leave the doe near the road to let the fawn come to it. It seems morbid but letting the fawn nurse the doe is the best thing for it until you can get it to an animal rescue center.
By now the fawn will be really weak from hungar as they need to feed several times a day. This may be the best time to find it as it may not be able to run away.
If you so catch it, cover its head and get it to the vet ASAP.
Good Luck