I believe things like birthday cupcakes are technically “pixie dust,” and not guaranteed, though I do believe they are quite likely in Magic Kingdom.
If you want to go the route of buying a celebration dessert to ensure you get one (or for something a little more special), every Magic Kingdom restaurant has a special paid dessert you can pre-order for celebrations. These cost $15 and must be ordered beforehand. Information can be found here:
https://disneytravelbabble.com/how-to/order-cake/magic-kingdom-specialty-desserts/
I got the link from the stickied cake thread.
I don’t personally think BOGs special option here is as nice as some of the other birthday options, though a chocolate rose filled with grey stuff does sound nice!
If you’re with a larger group or just really like cake, you can also order a Happy Birthday Mickey Dome cake. You’ll find the link to information for those in that same link. They’re $35, but they’re adorable.
The downside, frankly, to either of these options is that Be Our Guest is now a Prix Fixe meal that includes an already adorable dessert. It is nice to get someone something special for their birthday, so if she’s a big fan of dessert I say go for it anyway and have double dessert. If not, just appreciate the cutest little Chip cup made of white chocolate and filled with the grey stuff. Maybe get a special dessert at one of your other meals that day (or at some other point in the trip).