Actually "can't have done" is correct, though the two are not quite the same, grammatically. It is used to add weight to the statement, indicating that you are completely certain that something could not have happened at some past point in time. "She can't have taken the money! She was out of town at the time."

We can use both 'can't have done something' or 'couldn't have done' something to express past possibility or probability. The difference is in the level of certainty. 'She can't have done such a thing' = I am certain it's impossible She couldn't have done such a thing = =I think it is unlikely but I'm not certain.

No. "can't", or "cannot", is present tense, so it is speaking of what she currently can or cannot do. "have done" is past tense, speaking of the past. So to say "... can't have done...." is mixing the present and past tense. If you want to say "can't", then replace "have done" with "do". "She can't do such a thing" is correct, and speaking of what she currently cannot do. "She couldn't have done such a thing", is speaking of what she could not do in the past.