A 6 amp type B MCB will allow 30 amps before the magnetic part trips, it will in fullness of time trip at 6 amp with the thermal part, but I found with tungsten lamps if on failing you got ionisation it seemed to take the dimmer switch with it every time.
I suspect, even with a 1 amp fuse, it would still take out the dimmer, so no point in worrying about it.