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Looking at your plans, it should be easily done in 3 days with about 425 miles per day. If the weather is cooperative, you could head north on 89 to US 20 and get on I-15, then head up to I-90 through UT, ID, and MT. This is a beautiful way to go if your weather cooperates. To me, the biggest problem might be US-89. If worse came to worse, you could head out on I-40 west, and then cut up to Las Vegas and I-15 using the 95. It would add some miles, but a good weather alternative.
There are several alternatives, if the weather is not cooperative. Keep your options open. If you choose to find overnight accommodations ahead of time, ensure that they are the type that can be easily changed/canceled/modified. My husband and I prefer the type that can be cancelled up till 4 pm of the day of intended arrival, and would be held for very late arrival. It's kind of a peace-of-mind! With two cats, that would be highly suggested. That way you can find a place that accepts two cats before you leave home, instead of "on the fly". There are a number of places that accept pets, but some are picky about the type and the number of pets.
Let us know how else we can help!
Donna