They don't, thank you very much. Rabbits and eggs are both symbols of the fertility goddess Eostre/Ishtar/Ostara. Her symbol is also the moon, in which some cultures see a rabbit instead of a face. Eggs also symbolize the moon and are the ultimate symbol of creation and new life.The basket is a symbol of the womb in which this new life is carried.hey don't, thank you very much. Rabbits and eggs are both symbols of the fertility goddess Eostre/Ishtar/Ostara. Her symbol is also the moon, in which some cultures see a rabbit instead of a face. Eggs also symbolize the moon and are the ultimate symbol of creation and new life.