No, a field effect transistor will switch with almost no current into the gate, so their main advantage in switching applications is that they don't load down the driver circuitry.
They have very high impedance inputs. They can be destroyed by static electricity, so the gate shouldn't be allowed to "float," and there's some limitations on the gate that are in the data sheet for the part you are using. The maximum gate voltage for a lot of FETs is on the order of ~10 volts.
A junction transistor is probably fine for your application. They are somewhat more rugged. But unlike FETs they need current limiting into the base or they will overload the 555 or be destroyed themselves. For what you are doing, 1,000 ohms to 5,000 ohms is probably going to work.
Normally you'd calculate what you need based on the gain (Beta) of the transistor. Gain of 100 and that means the base needs 1/100 of the current that the load will impose on the collector - but look at the graphs, since gains are usually stated as minimum/typical/maximum for the part, and they change with temperature, and the amount of load. If you want to calculate it, but you shouldn't need a driver unless the buzzer has a problem.
What kind of buzzer is this anyway? A piezo buzzer doesn't need a lot of power, something like an electromechanical buzzer would draw a lot of current and a 555 probably couldn't drive it directly. Unless it is a bad buzzer (shorted).
A typical piezo buzzer uses from 5-100 milliamps depending on the part, and the 555 should be able to source that with no problem.
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The maximum output current is 200mA, this is more than most ICs and it is sufficient to supply many output transducers directly including LEDs (with a resistor in series), low current lamps, piezo transducers, loudspeakers (with a capacitor in series), relay coils (with diode protection) and some small motors (with diode protection). The output voltage does not quite reach 0V and +Vs, especially if a large current is flowing.
To switch larger currents you can connect a transistor.
NOTE!!!
The maximum output current of low power versions of the 555 (such the ICM7555) is much lower: about 20mA with a 9V supply.