저는 기뻐요 is commonly acceptable.
저는 기뻐해요 can be acceptable on below conversation:
A: 너는 친구의 성공을 기뻐하니 슬퍼하니?
B: 저는 기뻐해요.
http://www.howtostudykorean.com/unit-5/lessons-101-108/lesson-105a/
adjective+~아/어하다 can be used when the speaker is not the subject of the sentence, and is specifically used with words that describe a feeling that one experiences. Therefore, these would (typically) be incorrect by themselves:
제가 너무 부끄러워했어요
제가 너무 기뻐했어요
제가 너무 슬퍼했어요
제가 너무 부러워했어요
In the examples above, if I changed the subject to another person, the sentences would be correct.
However, it is acceptable to use the ~아/어하다 form of an adjective when the speaker is the subject of the sentence if there is an object in the sentence. For example, all of these are correct:
제가 가난을 너무 부끄러워했어요 = I am shy about/of my poorness (the fact that I’m poor)
제가 친구의 성공을 너무 기뻐했어요 = I am happy/glad about/of my friend’s success
제가 친구의 죽음을 너무 슬퍼했어요 = I am sad about/of my friend’s death
제가 남의 성공을 너무 부러워했어요 = I am envious about/of others success
It is actually possible to remove the objects in the sentences above, but only if the object can be immediately assumed from the context. This is essentially the same as changing 좋다 to 좋아하다 and 싫다 to 싫어하다. You couldn’t just walk into a room and say”
“나는 좋아해”
Instead, you need an object to specify what it is specifically that you like. For example:
“나는 과자를 좋아해”
However, if your friends were all talking about 과자, and were going around the room one by one and saying if they liked it or not, you could respond with just “나는 좋아해”.
In that same respect, you couldn’t just say the examples above unless there was some sort of immediate understanding of what object was being referred to.