How to find a replacement MOSFET
Look for improvements of the following parameters:


Id = 1 A (more is better)
Rds(on) = 10.5 Ohm (less is better)
Idm = 4 Amps - (More is better)


The following parameters should remain similar:


Vgs(th) = 2-4 Volts - Less than 2 Volt minimum is good, but not necessary
Vdss = 600 Volts - More is not needed, could perhaps go down to 400 Volts
td(on), trise, tfall, td(off) should remain similar or slightly lower than in the existing part's datasheet. 


Of these parameters, lowering the Rds will benefit you the most, resulting in less heat generated.

Based on the above suggestions, locating a suitable power MOSFET on a vendor's parametric search (such as on Digikey) should be easy.



Update: Reasoning behind key recommendations above:


Id, more is better: The existing MOSFET may have blown due to excessive current, beyond the specifications. Having more margin for error will reduce the likelihood.
Rds(on), less is better: The higher the on resistance, the more power (as heat) the MOSFET would need to while passing current - Power P = I^2 * R. Really hot = grilled MOSFET, medium-rare to well done.
Idm, more is better: Similar to Id above, other than in some circuit designs, the constraining factor is not sustained current, but current spikes going beyond the Id value but staying within the maximum intermittent current permissible. If this maximum was exceeded at some point during operation, such as due to a main power line voltage surge, that may have been responsible for the component failure.