Milan to Zermatt

It is almost 4 hours from Milan to Zermatt. For a day trip, that’s most of a day just to travel. It won’t leave you much time to “do” anything. The doing there is hiking or riding the scenic trains and lifts to viewpoints. Rick Steves’ guidebook is full of info on what to do. You can look at schedules at www.sbb.ch/en but use a date in the future, like mid-Sept, as right now the trains are not efficient between Italy and Switzerland due to track work so there are slower replacement buses and inefficient connections.

In addition to Laurel's comments, you will need to confirm much closer
to the date what lifts/trams/railroads are open. In the spring and fall,
many things in a mountain village close at some point for maintenance.

Then, you will need to figure out how to check the weather for the day
you want to go. You obviously don't want to go and have the Matterhorn
be socked in and impossible to see. In any case, mountain weather is
very changeable and you need to be prepared to be a bit disappointed.

I would not go for the day at that time of year. Zermatt is mainly for skiers - and lots closes in the between-times (spring and fall). That said, if it is running, you can take a train to the top of the mountain and on clear days, the view will be spectacular. I believe you will have at least two changes on the train, and you’ll want to check close to going as road repairs etc can make a 4 hour trip into a 7 hour trip. The old part of Zermatt is very charming but I would not go for the day from Milan. The lakes are fairly close and very beautiful - that might be a better day trip.

You travel by train Milan - Zermatt. You can book that on www.sbb.ch (but not yet.)
Most schedules will involve a change in either Brig or Visp, or sometimes both... But changing trains is a normal and expected feature of train travel. Should not put you off.