1300 watts at 12 volts equates to nearly 120 amps when you factor in inverter efficiency, probably even more with a budget brand inverter. This is too much for a simple leisure battery to cope with for the time scale of making a brew. Consider fitting at least 2 x Spiral Cell GEL batteries at a cost of nearly £500 or use a generator. If it was me, I would use a cafetiere on a gas hob. Much cheaper and a lot more efficient.