Is it possible to have perfectly secure public-key cryptography with oracles?
What you're saying is unclear... If you have uncountably many possible keys, if the scheme is computationally secure in the normal case (you're using an already-secure algorithm), your algorithm would fit your definition of being perfectly secure - the computation required to break it goes up with the key size, effectively creating an infinite search time for the key. The issue is, this basically equates to having a key of infinite size which is just as impossible to use for encryption, since the time to encrypt increases as well - just not as fast as the time to break it.
However, if we assume your oracles $A$ and $B$ operate in a finite amount of time (somehow you manage to encrypt using an infinitely large key) you would have a perfectly secure scheme, as you describe.