What state?
In most states, you do not do yourself any favors by having an "introductory" or "probationary" period. Either it's employment-at-will or it's not and by giving it some special name, it implies that perhaps the relationship is not at-will when this preliminary named period comes to an end. If you are employment at will, you can simply say they're not happy, they're speaking ill of the company, and they're violating the electronic communications policy (or whatever it is that you have saying you can't spend your day writing personal emails or hanging out on HR forums). Replacing people is an ugly chore, so perhaps a frank conversation would be better.
"Ms. Doe, it has been brought to my attention that you have been engaged in a lot of personal email use at your work station, so I've been monitoring your email. As you know, this is something you can get in trouble for but that's really not what I want to talk to you about right now. I'm saddened to learn that you are not happy here and you are looking for jobs elsewhere. Can you tell me what the problems are? Perhaps we can address them and, if not, perhaps this really just isn't the right place for you."
Either it'll get worked out or she'll quit out of embarassment or you start things in the right direction with an appropriate write up. Have you ever dealt with this kind of situation before? If yes: do the same thing again. If no, keep in mind that you are setting a precedent (assuming you want your discipline to be fair and have similar situations handled in a similar manner.)