Translation:My dad doesn't have hair.
头发 is hair growing on human's head. 没有头发 is literally having no hair (on the head). You can say 光头, which means bald or shaved, it's better than 秃头, since 秃头 is kinda offensive.
edit: for animals without hair you say 没有毛
Snake doesn't have hair. --> 蛇没有毛 shé méiyǒu máo
蛇不长毛 shé bù zhǎng máo
Sphynx cat is called hairless cat (无毛猫wúmáo māo) in Chinese
You can omit 的 in this sentence and any cases below:
的 is following a one-character word: 新朋友(new friend) ; 旧自行车(old bike) ; 好日子(good day) etc
的 is following a pronoun for person: 我爸爸(my dad) ; 她朋友(her friend) ; 我们老师(our teacher) etc
You can always bring the 的 back to make your sentence more formal or stress the noun after 的.