Designing a transformer with low usage time but high power output for small interval of time
Well, you would have to know how your breaker is set up... there is something known as inrush current and for about 3 line cycles you will go over the rated current, first cycle is around 25 times, then half that(12.5 times rated current) and finally down to a number close to rated current. This is approximate and not perfect. This only happens if you turn on the transformer and it was off.

So I would look up the curve of your breaker and the current you plan to run through your transofmer and see if it would trip it in the given time(3 cycles is around 50 milliseconds, depends on the frequency of your network) knowing the current and the time should be enough to find out if it will trip or not.

You want to avoid saturating your core as someone else already mentioned, if you have a BH curve or Vt curve available you can estimate how long it will take at a certain voltage for it to saturate and you should operate on a timeframe shorter than that to avoid overheating.