Your daughter already has dual nationality. It's automatic under Italy's Law 91/1992. She has exactly the same right to hold an Italian passport as anyone born to two Italian parents in Rome. (She can hold BOTH British and Italian passports if she wants to). Similarly she has the automatic right of abode in BOTH countries, irrespective of whether either or both of those countries are within or outside the EU. (As long as at least one of those countries remains in the EU then, as an EU citizen, she'll also have the right to live and work in any other EU member state).
Under the rules applying to dual nationality throughout the world, the Italian consulate can't help her if she gets into difficulties in the UK and the British consulate can't help her if she gets into difficulties in Italy. Apart from that, holding dual nationality (which, as I've stated, she has already) can't present her with any difficulties.