Although Italy's a lot smaller than Oz, it still takes quite a bit of time to get from place to place. There are fast trains between major cities and train stations are in the centers, but a lot of smaller towns are on minor train lines which means slower trains, connection times, and sometimes getting from station to center as well.
From Lake Como to Florence, you'll need to get to Milan to take a fast train. Bologna is a rail hub and a good place to base for day trips. It doesn't get nearly as many tourists as comparable towns because it doesn't have major attractions, but it does have a good historic center and great food. You could stay there and day trip to Parma, Modena, Ferrara, Ravenna, Padua, Florence, by train, then continue south. Florence is a good base for Tuscany. What do you want to do there? Visit hill towns?
Florence to Sorrento is about 500 km and will take you about 5 hours on public transportation, then at least 3, maybe nearly 4, to Rome - and that is from train station to train station. You'll need to go door-to-door which could easily add another hour each way. If you want to visit Pompeii and Naples, it's best to stay in Naples. Sorrento adds nearly 2 hours travel time and the main reason people go there is its convenience for daytripping. I'd only do this if Pompeii is a high priority. You'll need 2N in Naples so you'll have one full day there.
Count exactly how many nights you have. If you leave Como early, get to Florence around noon, 4N gives you a half day to see Florence and 3 days to visit other places. That's fine if you only want to use Florence as a base. But if you are interested in Renaissance painting, sculpture, architecture, you'll want at least 2 full days in Florence.
How many days in Rome depends more on your interests than anything else. If you just want to see the best of the best, 1 day for the Colosseum/Forum and 1 day for the Vatican w/its museums or a couple other "bits" w/o the museums. You could spend much much longer and still not see and do everything.
To get a better handle on transportation, use the official train websites, trenitalia.com and italotreno.it. Also rome2rio.com will give you suggested routes. Don't count on the accuracy, especially of timing. I used it for Sorrento and it only allows 19 minutes transfer time, which is ridiculous. It takes 10-15 minutes just to get through the Naples station to the local train ticket office and platforms. The local runs about every 30 minutes.
