A good anonymous question should be rewarded with reputation - to that account.
What you're asking is that you want a question that is not associated to an account, but that account gets to reap all the benefits from it. I'm not going to get into the programmatic and mechanical nightmares that would be required to set this up in the code, so let's instead look at the practicality and exercise.
Consider - every instance of reputation gain† is visible on your profile page, past the first point and the 100 points of bonus for association. There is no means to which reputation can be attributed to the parent account without the existence of a secret account being found - indicating unattributed reputation gain will be obvious, while just hiding it will raise questions about "ghost reputation" that people can only answer with "Secret account" (as that will be the only answer).
This is actually enough data for anyone to track down the associated ghost account purely with publicly available tools. All they'd need to do is isolate days in which the largest ghost reputation was gained (which will generally correspond to the original asking), then map out viable points where it could have happened.
†Downvotes you cast aren't shown, but this isn't reputation gain, and we are very public about the fact we hide downvotes to posts.
This is all a really long-winded way of saying if you want anonymity, and for questions to not be associated to your account and name, then they should be completely separate. Trying to get benefit for them means you have to own up to ownership of this anonymous account. Any means of a connection (reputation, badges, anything) is all public data that can be traced and essentially void the intention of anonymity.
Reputation is all about being recognized for contributions and claiming credit for it. This is counter to the very point of being anonymous and using an account that is not to be identified as your own, and so it would be a measured exercise of complexity that is far unwieldy compared the minor amount of benefit yielded to either involved party.