Just got the Killap Restoration Project a few minutes ago, and I saw there's a new feature that allows you to do some minor character appearance customization.

This is all well and good, but I can only choose two new hairstyles, and even though there's an option to change race; none are available.

Is there another patch I need to download?

Yep, there are only two hairstyles for males in F2RP 2.1.2b (a long haired and a bald dude). No race options either, it's an open feature for future versions of F2RP.

Modders are busy making new animation, though. See this link: http://www.nma-fallout.com/forum/viewtopic.php?t=50693

So there is no other patch. We just have to wait until Killap implements them in an update because I have no idea how to install these animations into the game.