In a common-emitter (source) configuration, a BJT will likely switch even slower due to storage time. The other suggestion of using an NC7WZ14 or any other modern fast gate (74LVC1G14, etc.) is more likely to do what you want. If you need more current than can be provided by a single gate, multiple can be paralleled through current sharing resistors, which can also serve the role as current limiting for the LED.