I'm not sure, but it would be something like that:
SELECT *
FROM (
SELECT unnest(ARRAY['CAT','CAT DOG CAT','DOG Cat']) AS Aminals, unnest(ARRAY[3,1,2]) AS SortOrder
) AS foo
ORDER BY SortOrder
See here:
8.14. Arrays[
^]
9.17. Array Functions and Operators[
^]