Translation:The rich woman has an angry parrot.
Erit is indeed the future of esse, but when you use the dative with it, meae puellae (which, whether you meant it as the dative or not,it still can be) it has a possessive meaning. As in, 'a dead parrot is to the girl'
You can read more about it here if it's a form you are unfamiliar with. It's quite common so it's good to know and expect: http://dcc.dickinson.edu/grammar/latin/dative-possession
Nick, I apologise for this: you have clearly invested a lot more time than is merited and was intended:
it is Genitive rather than Dative and is a mild parody - no pun originally intended - of a well-known work by a well-known Roman poet; he would surely appreciate Dickinson's advice, but I have kept largely true to his words.
For the record: the parrot (sparrow) of my girl will be (is) dead.
it was just a very quick swap to bring a familiar bird-based poem to current relevance but now olet lucernam and any humorous element may long have passed...
however, the commitment shown been most admirable and appreciated.