Is it true that it is only permissible – halal – for a father to change his daughters diapers/nappies during the first year of his child’s life and that it becomes forbidden – haram – for him to do so after that?

The problem is not one of changing diapers but of looking at a girl’s private parts. All jurists – mujtahids – agree that men may look at female relatives whom they may not marry – mahram; fathers and daughters for example, with two exceptions: They may not look:
a. at genitalia
b. with lust.
A father (or indeed brother, uncle, cousin, grandfather or any other male) thus clearly may NOT look, or in any way touch, the genitalia of his daughter (grand-daughter, sister, cousin, niece or other girl). No age is mentioned in the legal opinions – fatwas – of Imamiyyah jurists. The only instances when this might be acceptable are in cases of emergency when no-one else is available to undertake a necessary task.