Imogen is lovely, but
Ivy isn't. It's such an annoying plant, and the sound is unattractive. If she wants another plant name to balance
Rose, there are many better:
Daisy is cheerful and surprising, and
Felicia is good too - plus, blue flowers are so uncommon. Or, if she enjoys the repeated I, what about
Iris?
Amelie? With the French pronunciation, presumably. Seems odd with hyper-English
Imogen.
Emily is commonly used, but for a very good reason. I would have gone for
Emily Rose.
Emily and
Imogen seem better as a twinset than
Imogen and
Amelie.