I have a bryant gas pack with a White-Rogers Type 1F56-444 thermostat and I won't to replace the thermostat with a Hunter zModel 44860. Is this do able? And what surprises will I run into.

1st, I have to ask, WHY,is the WR tstat bad? It would not be do able in my house,I wouldn`t have a Hunter in my house they are junk.
The surprise you should look out for is most times when you install one, it probably won`t work
And if it does you shouldn`t be surprised when in the near future,about 2:00 in the am ,you wake up freezing your little tootsies off because the hunter has failed you

I would suggest getting a honeywell. Let us know what terminals are on the old stat and we may be able to help you choose.