I felt that maybe there is an alternate and concise way of saying She agreed to follow without asking questions in one(or two) word(s) ?
You can consider acquiesce.
to accept, agree, or allow something to happen by staying silent or by not arguing [MW]
The verb acquiesce comes from the Latin word acquiescere, meaning “to rest.” If you “rest” or become passive in the face of something to which you object, you are giving tacit agreement, you acquiesce.
Unquestioningly seems to fit your request; it's one word that means exactly what you describe. In some contexts, blindly might also be appropriate.
She agreed to follow, unquestioningly.
She agreed to follow, blindly.
While neither of those words indicate the presence of agreement or acceptance on their own, they do express the lack of questions. Depending on context, you could do away with the "agree" part and say something like:
She followed unquestioningly
However, if, say, the following is yet to come and the unquestioned act is actually just the agreement, then agreed unquestioningly is about as close as it gets without introducing positive/negative connotations or without introducing the possibility for questions.
If the context is about accepting or believing something, the idiom take at face value might be appropriate, but it doesn't fit the one or two word criterion.
"She agreed unequivocally" is another way that you could say the same thing as the (helpful) suggestions above.
The (dead?) metaphor rubber-stamp is often used in situations like this.
rubber-stamp (verb) [with object] Approve automatically without proper consideration: [P]arliament merely rubber-stamped the decisions of the party
Agreed wholeheartedly might be the word:
marked by complete earnest commitment; free from all reserve or hesitation. "gave the proposal wholehearted approval"
I think "she agreed doubtlessly" or "she agreed in a servile manner" fits what you are looking for.