Our trip from Autralia last year was just on $12k for 6 weeks. $3k was airfares.$5k was vehicle hire and the remainding $4k was for food,motel here and there,fuel camping and RV parks.
We worked on allowing $100 per day for fuel and meals,caming fees or RV park.It did average out at about that for the trip.
Living in a new country with a budget of $3k a month will be tight.

John