I think the answer depends in part on you, and in part on Venice. The season might also influence the answer.

Venice is terribly friendly to any kind of wheeled vehicle, strollers included. But you can traverse the (many) small bridges without tons of difficulty - - assuming that you are talkinag about a very ;ightweight ("umbrella") stroller.

A stroller does provide your back, shoulders and arms some relief when you are stationary - - as in, on a vaporetto, stopping to eat or drink or standing in any one place.

It will be more difficult in the warmer months (more crowded streets); easier in the cooler months, yet backpacking is warmer for your baby during the off-season.

Regrettably, I cannot advise you from personal experience. Only time I (we) ever traveled with an infant that age was to Yosemite, and to Hearst Castle. Those were (are) also non-stroller-friendly places. I thought we did fine without one. But then, on the other hand, we had a car. You will not.

Where else are you traveling? Plenty of other places in Europe are also not very stroller friendly. but if it works for you, you will find a way to get some good use out of it. Venice does not need to be your sole decision maker/breaker.

Best wishes,

Rex

Interesting that you should ask that particular question. While in Venice in September, we started chatting with an English couple who had a child about 9 mos. at an outdoor cafe. When they confessed they were completely lost and had only stopped because they were tired of going in circles to try to get back to their boat stop, we offered to walk them to San Marco and direct them from there.

I became acutely aware of the hassle of using a stroller in Venice. Though you would think that it is very flat, you have to remember that there are steps leading to most of the bridges crossing canals. We all took turns holding one end of the stroller while one of the parents held the steering end to lift the baby over the bridges. Though it wasn't strenuous, it was definitely a two-person job. For that reason, you might want to give yourself a break by also taking along a backpack carrier.

My neighbor spent 6 months there with 2 babies last year while her husband wrote a dissertation. She said they threw away their American stroller after the first week; it was too heavy, and the wheels could not take the strain. They bought an Italian-made super-umbrella model there that they still like best.
European strollers tend to be much better made for city use than ours are.
I now have two, I also found American strollers are not good for heavy travel use. Use your backpack, but you will want a stroller sometimes; make absolutely sure it reclines, but is very lightweight. Have fun!

If you choose to bring a stroller, buy a travel stroller. The Combi Travel Savvy stroller has a canopy, basket and reclines, but folds up very compactly and weighs only about 10 lbs. Sturdier than a umbrella stroller, but much lighter and more maneuverable than a regular one.

Some Combi strollers also allow you to attach a carseat to them (like those Baby Trend ones), which is handy. But they aren't good if you or your husband is tall.

People who bring infants with them to Europe are morons! The infants have no idea what's going on, and the parents simply annoy the rest of us. If you can't bear to be separated from the child, then stay home with them, and leave those damned strollers home too - I'm sick and tired of being smacked in the legs by them.

Yes, let's just do away with this having babies altogether.

All of xxx's complaints will be over in - - say - - a hundred years or so.