Hi!
As mentioned above, 1/2 amp on 240, but 10A draw on 12V, but your inverter will be taken the 12V and upping to 240, i'm not too sure on the current draw in this scenario, but i guess it's much less than 10A. One thing, your inverter may be 300W, but that's maximum, maybe peak to peak load, so in real terms could be 150W continuous? You may be overloading the inverter?
Here is a online calculator which is easier than trying to do the math for current and power in your head. It's all simple ohms law - you just have to remember the formula
http://www.the12volt.com/ohm/page2.asp" onclick="window.open(this.href);return false;
Another thing, is 120W gonna keep you warm? It's only 2 normal light bulbs after all? Maybe you would be better with a gas heater or use a hob, you can get both with disposable canisters, and then maybe use the inverter for other things like running the radio, charging the mobile phone, and running the laptop?
Though saying that, it may well just take the chill off overnight of you have little ones?
Cheers!
Alistair