Step 1 (Understand the grammar rule).
The adjective "allergic" is always followed by the preposition "to" when indicating the substance or thing causing the allergy. Step 2 (Check each option).
(a) "in cats" — incorrect usage with "allergic".
(b) "with cats" — incorrect collocation.
(c) "at cats" — incorrect preposition here.
(d) "to cats" — correct collocation: "allergic to cats". Step 3 (Construct the sentence).
"She is allergic to cats" is grammatically correct and idiomatic.
\[
{\text{to (Option (d)}}
\]