In the context of MP, as I understand it, Fanny's amber Cross is very explicitly a religious symbol of (Anglican) Christianity, and of Edmund and Fanny's shared beliefs. The moral symbolism of this Cross as Fanny's only ornament would have been obvious to JA's contemporary readers.

I think the sort of Cross which JA had in mind would have been similar to the topaz Crosses which she and her sister Cassandra received as gifts from their sailor brother Charles Austen. A picture of these crosses is linked below.