"갑자기 딸기가 너무 먹고 싶어요.", it's right. :)
Speaking of using "가", it's because the syllable of word, which is "딸기", didn't end with consonant but vowel. For instance,
In the case of ending with vowel,
-> 복숭아가(or 복숭아를) 먹고 싶어요 : I want some peach.
-> 친구가 보고 싶어요 : I want to see my friend.
In the case of ending with consonant,
-> 수박이(or 수박을) 먹고 싶어요. : I want some watermelon.
-> 부모님이 보고 싶어요 : I want to see my parents.
FYI, when the last syllable is a consonant, you can use 은/이/을, but when the last syllable is a vowel, you can use 는/가/를.
:)