Replace Transistor with Mosfet?
You haven't said what voltage you're driving the gate from, but this should work fine. If you take a look at figure 5, you can see the maximum current the FET can conduct at different gate drive levels; at 3.3v gate drive it can conduct just under 200mA.

Note, however, that unless you can guarantee that your gate will never be floating, you should include a pulldown resistor to ground on the gate. Otherwise, when the gate is floating - for instance, because the MCU it's connected to isn't initialized yet - it can take on any value, and may turn on or off unexpectedly.