I haven't been through this yet, as I've not transitioned in public at all, but I don't see the reason to tell them before your appointment. Did your friend have any reason why you should do that, or was it just that she didn't think it would cause a problem?
My inclination would be to wait as long as possible, only sharing the information when necessary to provide time for HR/management to react and make any necessary plans to support you. If they've had transgender employees in the past, I would think they know the drill to some degree. I suppose if I thought I might be inadvertently outed, that might be a reason to go through official channels earlier rather than later.
On the other hand, you sound like you're on a pretty well defined path, so maybe there's not much reason to wait, either. In any event, I don't think any appointments, treatments, etc, are germane to the decision about when to talk to them.