Italy can't really be accused of being a nation of 'daddy's girls', mainly because the Italian language doesn't even have a specific way of conveying that label. One suggestion would be to use the similar phrase cocca di papà.
On the other hand, a mammone (or 'mother's boy') is a very common phrase used to describe boys who are over-dependant or over-attached to their mothers. Perhaps this fact reflects the maternal nature of Italian culture.
Cocca di papà
Cocca di papà is one of the most common phrases used to describe a 'daddy's girl'.
The word cocca is Italian for 'darling', which actually comes from the word coccolare meaning 'to cuddle'. In this context, the phrase cocca di papà translates to mean 'daddy's darling'.
Papà and papa
It's important to make sure the accented à is pronounced properly in the word papà (pap-ah with stress on the last syllable). This is because Italians may confuse a mispronunciation with the word papa (pah-pa) which means 'pope'.
Ragazza di papà
If you're using one of those free online translators, you may get the literal translation of daddy's girl which is ragazza di papà.
Whilst ragazza does mean 'young woman' or 'girl', it is often used to describe a girlfriend. To avoid labelling yourself your 'father's girlfriend' it's best to stay clear of this translation.
Another pitfall to avoid is the temptation to take the morphology of mammone and apply it to the Italian word for dad, which is papà. Unfortunately, the word pappone is already used to describe a number of things- none of which a daddy's girls would want to associate with her father (hopefully!).
The first meaning of the word pappone is 'a person who is gluttonous'. If this wasn't bad enough, the second meaning refers to someone involved in 'expoliting and protecting prostitutes'.