I keep my birthday, not birth year, secret (except from my parents and husband, obviously) so I can spend the day however I want. I'd be very upset to suddenly be forced to have a birthday party just because it's what some other family members or friends want. I've seen threads here on a similar issue, which is that some like to force surprise parties on others and just cannot understand why that would upset someone.
If you can't let the day pass in peace, as the birthday girl wishes, then I agree with the idea to send her the Ipad cover in the mail. That way she can privately deal with the disappointment of having accidentally let her secret slip. If you confront her with your knowledge in person, in the form of a gift and cake, she'll have to smile and pretend she's not unhappy.
Most importantly, think about why you're doing this. Is it really for her or do you want to flaunt your discovery and use social norms to make her miserable while you get to pretend to be the better person?
Edited to add: After posting, the first thread I saw was "Dear Prudence: My MIL redecorated my house." It's the same situation. The MIL did something "nice" for the son and his girlfriend, but it was really passive-aggressive. The girlfriend can't even complain freely to her friends, because some see it as "nice".