Right you are: (2) is incorrect grammar. Now, you see, we have changed the usage and the subject. Previously it was 'something'-- not the agent-- 'needs to be done / needs doing'-- by the agent: 'the housework needs doing / needs to be done by the maid'.
In the current case, the synonymy between 'to need doing' and 'to need to be done' no longer applies; we are now facing the q