Her new school will have known her current setting from your application, schools get this information from admissions.
They won't have just turned up, they will have arranged the visit with the nursery to check if it's a convenient time so if you're going to be annoyed at anyone for not telling you in advance about the visit be annoyed with them, not the school! Not that nursery have done anything wrong either by not telling you in advance imo. I'm assuming you haven't told them that you've been keeping it quiet to your daughter about where she's going to school in September? That's on you I'm afraid. They're not to know it was a 'secret'. It is the job of the nursery and new school to work together to help make the transition as smooth as possible for your daughter. They're doing that, as meeting the new teacher in a setting they're already comfortable in is part of that preparation.
You are doing her a disservice by choosing not to talk about it until now. You've lucky that, at her age, she probably won't have twigged that this teacher was only visiting her and not everyone. She needs to know where she's going though and the fact she'll make lots of new friends. Walk past the school together, talk about her going there. Surely she'll have some visits there before September? You were never going to get away with pretending she's going to the school attached to her nursery until September. Poor girl would be so confused if you left it that late to talk about it.
It's madness that you think schools have time to personally ring you, the parent, to arrange visiting your child at their nursery. For one, they wouldn't dream that someone is keeping it from their child that they're going to be attending their school!
It's a massive positive that this has happened, so you can now be open and honest with her.