First, find element resistance:
Resistance = (Voltage x Voltage) / Wattage
In the case of most water heater elements, the voltage at which their power is rated is 220 to 240 volts (its usually 240v). For a 1500w element, its resistance is therefore between 32 and 38 ohms.
Second, find the current draw at the new voltage:
Current (in amps) = Voltage / Resistance
In the case of a 1500w element operating with 120v, the current is: 3.75 to 3.15 amps.
You should now see that a 1500w element is no problem for a 15a circuit. I would upsize to at least 4500w (9.4a @ 120v) and you could also go with a 5500w (11.4a @ 120v) element. They should be low or ultra-low density elements to reduce any chance at wort scorching, although scorching is unlikely if a PID is used and setup properly.