This charming bottle belongs to a group of bottles of naturalistic forms, mostly carved from this sort of distinctive chalcedony, which has been tentatively attributed to the Official School (see Moss, Graham, Tsang, A Treasury of Chinese Snuff Bottles, Vol. 2, Quartz, no. 258, and the several subsequent examples which are all attributed to the school).
In Hidden Meanings in Chinese Art, p. 70 and 76, Terese Tse Bartholomew illustrates a drawing of another snuff bottle which she attributes to Suzhou. She explains that the jujube (zaozi) is a pun for 'early son' and the peanut (huasheng) is a pun for 'giving birth.' The combination of the two suggests the expression, 'May you soon give birth to a distinguished son' (zaosheng guizi).
Bartholomew further explains:
"The peanut plant (Arachis hypogaea) has a massive root system and bears many seedpods, or peanuts. Thus it symbolizes long life and many sons. The peanut is also called chuangsheng guo, or the fruit of longevity. Along with jujubes and chestnuts, it is among the dried fruit and nuts scattered on the marriage bed to wish the new couple the speedy arrival of sons."
Another very similar jujube-form agate bottle carved with peanuts is in the Palace Museum, Beijing and is illustrated in Snuff Bottles. The Complete Collection of Treasures of the Palace Museum, p. 165, no. 255.