「これはだれのぼうしですか」 is right.

The 2nd one. The first one is asking, "who is the hat?"

Just more info. You have to write ぼうし but it's often pronounced ぼおし. It's confusing for learners. I'll give you another example. がっこう（school). it's pronounced がっこお。Boy's name、たろうis pronounced like たろお。 これは 誰の（だれの）帽子（ぼうし）ですかis correct. it's not かばん（bag). Sayaka's answer is right. And you cay say, このぼうしは、だれの（だれのもの）ですか too.

この帽子は誰のですか? or これは誰のかばんですか? good luck!