Living in Italy with Italian and Maltese passport

My husband and I plan to live in Italy for 1 year. We are Australian but I have an Italian passport and my husband has a Maltese passport. We plan to have an income coming from Australia as well as doing some online teaching work although we are also open to doing some work locally if available.
What do we need to do to legally live in Italy? Do we need to apply for residency? What is needed to apply for an apartment to rent? Do we need an Italian bank account? Can we apply for local healthcare or would we need health insurance.
Appreciate any advice. Thank you!

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As you each have EU passports, that is the first hurdle you don't need any visa to live in Itlay.

The basic principles for an EU citizen moving to live in another EU country are the same throughout the EU. More information can be found on the official website of the European Union.

To remain in Italy for up to 3 months, you can report your presence on Italian territory to the nearest police station or Questura (dichiarazione di presenza sul territorio nazionale).

If you intend to remain in Italy for a period exceeding 3 months, you must apply to your nearest town hall (Comune - Ufficio Anagrafe) for residency (iscrizione anagrafica). You will be issued with a certificate (attestato d'iscrizione anagrafica), which is valid for 5 years from the date of issue, or for your period of intended residency (if this is less than 5 years). After 5 years EU nationals can request permanent residency (attestazione di soggiorno permanente).

You should enquire at your local Town Hall (comune) regarding the documentation necessary to apply for residency.

After three months in Italy, applying for residency is essential if you wish to access various services in Italy, such as free healthcare.

You can also read up more on Expat.com Guide to Italy HERE.

Thanks so much for the replies.  I have been reading about healthcare but I'm still confused. As EU citizens I understand that we can apply after 3 months as long as we have a residence permit and codice fiscale. We probably won't work locally but will get an income from Australia. What I'm unsure of though is whether this is the voluntary registration which we pay an annual fee for or whether it's free?

Hello, we are Americans with Italian passports. Once you have the residency in Italy after the 3 months while you can stay without a visa, you will be also considered a taxable citizen living in Italy, regardless from where your income is coming from (we have income from the States). Perks are that the social medicine is available also during the 3 months that you are in Italy without an established residency( as Italian it is available, social medicine is given to all citizen with or without residency). The difference is once you are a resident you will have a card (tessera sanitaria) and a doctor allocated to you (medico di base) to whom you can go as much as you need to free of charges.  Also you will be put in a  category where your percent of services are established (for example you need blood work, you'll have to pay a ticket depending on your income). I know that living in Malta might be a more favorable as per tax situation, in Italy taxes are high but you should be able to get a credit to your Australian taxes, there are laws for the purpose to avoid double taxation. Every individual's tax situation is different, I suggest to invest in a meeting with an expert international tax cpa or lawyer to avoid surprises.  Medical, social medicine etc. are linked to the taxes and you need to understand your benefits and your obligations as a resident and citizen.