The context places this chapter in the early Meiji, or latter half of the 19th century.
Traditionally in China and Japan, a child was counted one year old at birth, and then a year older every lunar New Year. So, technically, a child born in December could be 2 years old a month later.
In Tonari no Totoro,
Satsuki falls into Totoro's burrow at the foot of a giant camphor tree.
青柳 [あおやぎ] Aoyagi
鈴 [すず] Suzu
風呂敷 [ふろしき] wrapping cloth, cloth wrapper
虚海 [きょかい] Kyokai
慶東国 [けいとうごく] The Eastern Kingdom of Kei