"We love cooking Chinese food."
I would not say it is wrong, but it is really not quite natural indeed. We seldom add 的 in the phrase "Chinese cuisine", as it is almost a compound noun.
After all, personally I don't think that foreign learners should have an unproportioned concern on the matter of omitting 的, as it rarely would make your sentence so wrong that it is incomprehensible (not that it never would). Correct sentence syntax for example is much more important.
For the matter of omitting的, please make reference to this thread. https://www.duolingo.com/comment/25480888