We are expecting our first baby soon. We live rural and it will be around a 1 hour 45 min drive home from hospital, the final 10km are a bumpy dirt road. What are the recommendations for safety during lengthy travel and bumpy roads?

Red Nose has the following recommendations about baby sleeping in a car safety device.
Once the car journey is over it is very important that you remove baby from the car seat or capsule, even if this means waking baby, because it is not safe for baby to spend long periods in car seats, capsules or infant seats.
https://rednose.org.au/article/are-there-recommendations-for-car-seat-or-baby-seat-use

There is no specific time that represents “long periods” , however when driving for extended periods, it is recommended by Road Safety organizations to stop & rest (& stretch) every 2 hours.
During this rest time, take baby (&/or toddler) out of the car seat & place them flat for sleep (if baby is sleeping)  or hold/lay baby in a neutral position. Allow a toddler to “run around”.