Yikes, that seems like a lot to heat one room. Have you considered going to an electric mattress pad? They pull WAY less power than that heater. Then you could put your heater on a timer so it doesn't have to run all night long.
Here is a great example:
ElectricMattressPad
On the highest setting it only uses 43W vs the oil heater that is using 1000W.
If you could just run the oil heater for say 2 hours before you get up, you could save yourself 5.75 kWh per night. For most of us, that is around $0.70 a night. After a year you'd be $255 ahead minus the cost of a mattress pad which is like $50-100.