Problem (Present Perfect)?

Tom用present perfect tense問是可以的，因為他的問題是假設"你現在這時已經吃了晚飯，而想確定/問清楚。"

你回答的主句"I have not had dinner"亦正確回答他的"假設"時空情況。
只不過句前的修飾詞或形容詞"Very early"則不是合格的英文，正確的回答應該是"It is very early,"或"It is too early,"

另外Tom是男性，何解你寫句「我答的是"她"」？

in my opinion,Tom's QUESTIONS is correct,but your answer"very early" could be better.
依筆者拙見，湯姆的問題是正確的，但您的回答「太早very early」可以改進。
因為您用的結構是"因為太…A…而不能V"
why not say
"it's too early to have dinner "
（現在去吃晚飯還太早）
Or "No,I have not had dinner yet.it's too early."
（不，我還沒吃，現在還太早）