She must be tired from running around all that time, now she's been sleeping since I put her in her car seat.
この場合、次のような言い方ができますよ。
ーShe must be tired from running around all that time because she's been sleeping since I put her in her car seat.
「彼女はずっとはしゃいで疲れたのか、カーシートに乗せてからずっと寝ている」
to be tired from running around で「はしゃぎ疲れる」と言えます。
ご参考まで!