If from Zurich airport expect difficult driving and traffic jams when leaving the airport on motorway due to major road works, later afternoons mainly. Shortcut from airport via Zurich city is feasible but not recommended.
Make sure you are familiar with driving rules in Switzerland.
Thanks for the info
And absolutely check weather conditions before deciding to drive in the mountains. And as you say this is next week, make sure your care is equipped for winter (tyres and eventually snow chains). The forecast is for snow from Tuesday on in higher elevations. And should you need to put on chains, don't wait too long and do it on the road. Get off somewhere flat to put them one, otherwise you block the whole traffic.
The route we normally take to St Moritz goes via Zürich - we take the A3 to Landquart and then drive up to Klosters. Put the car on the train through the Vereina tunnel and then drive up to the Upper Engadin. It is a lovely drive. Will take you about 3 hours not including waiting time for the train if there is any.
But heed Engadiner's comments about snow. The Engadin is very high (1800m on the valley floor) and it gets a lot of snow.