You can already mostly do this by abusing the URL processing algorithm, but it's an extra step to get the URL (you'll have to manually edit).

How? When you put in an *answer* post ID into the URL where it expects a *question* ID, you get taken to the answer automatically!

Example linking to Jeff's answer:

Long link (from the "Link" button): http://meta.stackexchange.com/questions/63841/show-a-short-link-for-answers-too-not-just-questions/63846#63846

Short link: http://meta.stackexchange.com/questions/63846

Using the shorter link, you automatically get redirected to the long link.

<strike>The only way I could see this getting shorter is something like http://meta.stackoverflow.com/p/ ('p' is for posts) followed by either a question ID or answer ID.</strike> Edit: this is already implemented as /q/.