While there's some precedent for it in the form of Software Recommendations, keep in mind that Anime SE is already a small community by SE standards. In addition, I suspect most of the regulars would not be too interested in such a proposal at this time, considering we still have some of our own quality issues to work on (though overall we're doing well for a beta site). In my opinion, we're still in need of more experts on Anime SE, and it doesn't seem like a good use of our efforts at this time to try creating another site rather than improving the one we already have.
I'd say wait a while to see what happens with Software Recs and if any other sites are proposed e.g. "Video Game Recommendations" (which would be more natural given that Arqade is easily 10 times larger than Anime SE). There could also be some broader site like "Fiction Recommendations" which would alleviate the need for an Anime Recs SE without any work on our part. There's still a lot that needs to be worked out before recommendation-based SE sites have been demonstrated to be workable, and we should let the larger communities on SE test the waters first before devoting a significant amount of effort to this. Waiting also has the benefit that in that time, Anime SE will have more chance to grow and likely graduate, so you'll have a broader audience to promote this to initially.
That doesn't mean I think it's necessarily a bad proposal, but at this point we're still too far off from it being a reality to be worth proposing. If you do propose it now, I'm fairly confident that it won't make it through the Area 51 process to beta, either from lack of interest or from some moderator closing it.
For now, the Anime SE policy of referring users asking for recommendations to chat works decently. The chatroom is relatively active and there's almost always someone willing to offer advice. There are issues with that, but those are more a topic for Meta Anime SE than here.