Venice to Zermatt

It is possible, but not really practical. Consider taking the train instead. There four good reasons:
1. if you are renting a car in Italy and dropping it in Switzerland, the drop fee may be quite expensive
2. you cannot drive in Venice, you will have to leave from Tronchetto at best
3. you cannot drive in Zermatt, you will have to leave the car in Tasch and take a train
4. train will be running in the Simplon tunnel while you will have to drive the pass.

Take the train. The train journey takes as little as 6 hours54 minutes.

Driving involves renting a vehicle (careful to not put a scratch on it as you will pay dearly), expensive petrol, pay your tolls along the way which can really add up, stop at the Swiss border and purchase a Vignette for the car (allows you to drive legally in Switzerland), pay for parking when you get to Tasch because you can't drive all the way to Zermatt, pay parking every day your useless rental car sits unused while you enjoy Zermatt. You'd better return that rental vehicle to Italy or you'll pay $$$ in extra drop charges for foreign country drop.

Just take the train.

also have a look at this:
https://www.tripadvisor.com/ShowTopic-g188098-i858-k6650622-Driving_to_Zermatt_from_Venice-Zermatt_Canton_of_Valais_Swiss_Alps.html

I have no choice, this trip is only one portion of visit. Is there an auto train?

Mal, no there is not an Autotrain (by which I assume you mean a train you can put your car on). There are very few of those.
Yes, Venice to Zermatt can be done in one day. viamichelin.com says 498 km ~7 hours plus stops, it will be slower and less comfortable than the train. But there are plenty of nice places to stop if you want to, starting with Stresa.

As others say, you will have to leave your car at Tasch and get a train the last section up the valley to Zermatt; and pay parking fees while you are in Zermatt. You will need to pay Italian Autostrada tolls, and the Swiss CHF 40 Autobahn Vignette. And, if you are not returning the car in the same country you picked it up, a one-way hire fee.

When are you doing this? If it is winter, the Simplon pass and the valley from Visp up to Zermatt will be "interesting"!

Mal - you say you have no choice. WHat does that mean? Are you saying you will already have a car when you arrive into Venice so therefore you must keep it? Where do you pick up your rental car? Where are you dropping? And what are your destinations in between?