Is there any way to do this in Quest? Not been able to find anything.

Nope, but why do you need to?

I want to have a Text Processor functionality that will call a function, and I want to be able to deal with the function not existing.

try {
  return (eval (function + "()"))
}
catch {
  return ("[Oops, function does not exist]")
}

Is there any benefit to having the text processor calling an arbitrary function? You can't pass any parameters in your approach. Why not just concatenate the function result and call it in the usual way?