Induction doesn't sound very powerful. I just went online and converted 1800W to BTUs. It came out at just 6100! Surely that's not enough to cook?

The "pure" conversion does not take relative efficiency differences into account. Gas burners are typically only 35-45% efficient (which is why commercial kitchens using gas are often so hot). Induction cooktops are anywhere from 80% to 95% (depending on how it's measured), but as a rule of thumb, an 1800W induction unit is the equivalent of 16,000 BTUs of gas.