Hi Lilia,
Any time is a good time to travel with a child as long as you're prepared. We live in England, my family lives in the Bay Area and my husband's family lives in Australia, so we have travelled A LOT with my now nearly 2 1/2 year old - including a round the world trip when he was 18 months. If only babies could get frequent flier miles...
I'd be happy to answer any specific questions you might have, so feel free to email me , but off the top of my head here are a few recommendations:
1) If you can afford it, get your child their own seat. It will give her a place to play and sleep and will make SUCH a difference to the experience you all have.
2) That said, I wouldn't get the 'car seat' that the airline will offer for the journey. You will have to have the baby on your lap with a special lap belt that they provide for take off and landing, but then she can move around freely in her seat and lay down on it when it is time for her to sleep. Trust me, you will be thankful for the space.
3) Come prepared as much as you can with her full bedtime routine on the plane. If she usually has a bath, then changes into her jammies, then has 2 stories, a bottle of milk and sleeps under a particular blanket or has a stuffed animal she sleeps with then do as much of that as you possibly can. Take her to the bathroom for a wash, change her into her jammies, read her the same stories she has at home, give her the milk, etc, etc. My little boy sleeps beautifully on planes - usually 8 hours from London to SFO and 13 hours on the 25 hour trip to Australia - and I think part of it is because of this.
4) Don't worry about flying direct. If you can that's great, but if you need to change planes along the way it can be a good thing. It will give her a chance to stretch her little legs. Another thing, even if she's not walking, let her crawl around the airport (obviously in a safe area). She will get dirty, but just have all the necessary antibac wipes and things to clean her up ready. If she has an opportunity to burn off some energy, you'll all have a better continuing journey.
5) When you get to your destination, get her on the local time immediately. She'll be excited to get there, so she'll probably happily stay awake until her nap/bed time. Put her to bed and if she usually has a 2 hour nap but she is still sleeping soundly after the 2 hours, wake her up. She may not be happy at first, but trust me you'll both have a better trip the quicker she adjusts. Put her to bed at her normal bedtime. She will probably wake in the night. If she does, keep the lights dim and any activities really mellow. When my little boy wakes up, which he usually does for 3 nights, we either watch an hour of a quiet video or read some stories for an hour or so and then I put him back to bed. He'll then usually sleep until a pretty normal wake up time.
6) If your child likes TV or videos (mine LOVES them) get a portable DVD player. This will come in handy on the plane, but also if you need a little peace in the hotel. There won't be any English TV in Italian hotels. There are two things to pay attention with the DVD players - battery life - a 2 hour battery life will do you no good on a 15+ hour flight to Italy. Also, come prepared with the necessary converters so you can plug it in in continental Europe.
7) I also used to live in Italy. I didn't have my little boy there, but I nannied, so I had a lot of the same challenges. You don't say where you're planning on going in Italy, but I personally would avoid Venice with a stroller. It can obviously be done (people live there and manage) but if you really want to go to Venice, I would invest in a good Baby Bjorn or other carrier/backpack. It will make it much easier getting on and off boats, over the multitude of bridges, etc.
8) The other thing worth noting about Italy is that a lot of the streets are lovely but very stroller unfriendly cobble stones. If you can manage to bring a stroller with pumped up wheels rather than hard wheels your little girl will have a nicer ride.
9) If you're renting a car, most places will provide a car seat for an additional cost. Make sure you pre-book, call to confirm and get this in writing. The Italians have a very 'oh well we don't have one, you'll just have to do without' attitude toward such things and may treat you like a hysterical mother for insisting. Trust me, the Italians drive like maniacs, so you'll want a car seat!
10) That said, the italians love kids and you will generally find them very accommodating. They accept that children make noise and mess and will be more than happy to help in any way they can to make your trip enjoyable. I love the Italians.
11) Most grocery stores (supermercato) close from Saturday afternoon until Monday morning, so if you're going to arrive during that time, make sure you have all the snacks and things you need. You can usually get diapers and formula at pharmacies (farmacia) which you should be able to find open. You can ask at your hotel for where the local one is that is open.
Sorry I'm rambling and giving you way more information than you asked for. I got a bit carried away. Like I said, if I can help with any specifics, please feel free to email me. I'm more than happy to help.
Enjoy your trip. Relax, just prepare as much as you can and then leave the rest to adventure. Your little girl will love it.
All the best, D.