。
She's been wearing the same hat for a month.
Literal
She [topic-は] one-month same hat [object-を] is-wearing.
一ヶ月 (いっかげつ) — note the small ヶ, a counter ligature derived from 箇 (also written 個 or 个), used almost exclusively after 一, 二, 三, etc. for periods or counts of objects. 帽子をかぶる: かぶる is the specific verb for putting on something covering the head — distinct from 着る (clothing on torso), はく (legwear/footwear), and つける (accessories). ~ている here is the ongoing/habitual reading: she has been wearing it on every relevant occasion across the month.