I think that this brooch (posted originally by Beth above) was most likely a gift to Princess Elizabeth for standing as a bridesmaid for Mrs. Vicray Gibbs (nee Jean Frances Hambro) at her wedding to Andrew Elphinstone.
The maid of honour was Margaret Elphinstone (later Margaret Rhodes) and she can been seen in wedding pictures wearing the same brooch.
It also then makes sense why Princess Elizabeth would wear the brooch at the chrsitening of their daughter.