As there is no other major devices connected along with the timer IC you can go for it. Don't want to worry about the source and sink currents at this particular application.
hi V,
Driving the IRF320S requires a voltage drive with a small current, so the TS555 should work OK.
I would suggest a 1K series resistor from pin #3, Output to the MOSFET gate, just in case you have a FET failure, it should prevent damaging the TS555.