Is there a way to type Niqqud on iOS? On my iPod touch I am able to type basic Hebrew characters by adding a Hebrew international keyboard.

Is there some way for me to type Hebrew vowels (Niqqud) [without using any specialized apps]?
I think not, only by using a hardware keyboard or via copy/paste from another doc or an app like Unicode Maps.  You might be able to make a custom layout as well with Unicode Maps.  Also have a look at Keyman.

A 3rd party keyboard is Davka Nikud.