You're right, it does show up below the question with the other links:
But it's not always available. As described by Taryn here:
the question must have at least one answer by a new user aka a user with < 10 rep on the site (which is the required rep limit to answer protected questions).
If the question does not have an answer meeting this requirement, then the protect option will not be available. This should minimize some of the protecting of questions that do not need it.
The theory is that questions should only be protected when there's evidence that they need it due to low-quality answers from users that would be stopped by the feature.
A quick scroll through the answers on that question confirms that none of them were posted by users who
would have been affected by that restriction would currently be affected by that restriction. Of course, as a user who would be affected by that restriction, I don't have enough reputation to confirm that there aren't any deleted answers. But since you're not seeing the option, I assume there aren't.