We did this recently with similar aged child, the journey was fine and the holiday was great. Some tips, hope some are relevant. I travel a fair bit for work with DC in tow.
You can usually check in 2 pieces of luggage for an infant from stroller, car seat, booster or travel cot.
If you bring a stroller you can keep it until the gate. We have a travel bag for ours and stash some extra nappies /wipes in there.
If hiring a car we usually bring our own car seat after a stressful experience with a car hire company.
A baby carrier is handy (but was possibly more useful when smaller) for when you get off the plane and might not get stroller back until baggage reclaim. Of you're lucky it might be waiting for you when you get off the plane. In Gatwick we had to go through security first and the queue was very long.
Depending on price and duration of flight it might be worth buying an extra seat for the baby. Have done this a few times but not always.
Pack enough clothes for the flight and then extra outfits and nappies in case of delays. Easy up and down shorts or trousers are good for nappy changes in a tiny plane toilet.
Most people are helpful or at least tolerant. Don't piss them off by letting DC kick their seat or pull their hair etc.
Bring liquid paracetamol and any medication you use for your child.
Italians are generally welcoming to children and will make a fuss of them. This is your holiday so let routines slide a but and have fun.