I noticed my gold answer (along with the question) was moved to the Meta site. Shouldn't my points and badge be moved here as well?
Your badge wasn't moved, it just clocked in Meta for when the question itself was moved and your answer was counted.
Your points wouldn't be moved because they don't mean the same thing out there in the wild SO than in Meta.
it doesn't seem like your badge was moved, more like you got another one. your badge on SO still exists.
I don't think the points will be, but the badge will (hence my "great answer" badge here, for the Jon Skeet Facts question).
I wonder if when a rep recalc is called you will get the rep from a migrated question, or if it intentionally skips over migrated questions (which doesn't make the most sense).