Spazz, so sorry. You're probably sick of hearing that but sounds like you're getting on with "stuff." What about school? Are you transferring?
Don't know total transit but Salt Lake City to Sacramento can be done in 10-12 hours with a pooch. Variables include the driver's need for breaks. the vehicle's aerodynamics, the snow/ice and the pooch's curiousity as opposed to urgency.
Could you take a more southern route to avoid the really bad weather? Even Nevada ain't so easy in the winter. Besides, if you take I-40 you could see Amarillo!
If you do decide on I-80, avoid Reno/Tahoe Friday-Sunday.
Frends know gud humors when dey is hear it. ~ Da Crockydiles of ZZE.