Yes, I think it's a great idea to drive from Dallas to SLC.
As many have already advised, your proposed route through Wyoming isn't the best way to go. I've driven coast-to-coast over 30 times
, and I-80 through Wyoming stands out as one of the most hypnotically boring stretches of road imaginable. The weather should be OK this time of year, although there are frequently crosswinds - often strong - on much of that stretch.
I've also made a longer version of your particular trip (starting in suburban Houston, then through Dallas and Salt Lake to Boise, ID) three times in the last two years, because we're probably going to relocate to either Colorado or Idaho in the future, and we're trying to experience both places in all seasons. I'm about to do it again in July. Trust me...I-35/I-135 through Oklahoma and Kansas, and I-70 through Kansas and eastern Colorado, is almost as incredibly monotonous as I-80 through Wyoming.
I've got a route that I think you'll enjoy much more, if you are interested in a variety of scenery. It's actually (very) slightly fewer miles as well, though in total it takes a few hours longer because it's not all interstate highway. About the only reason to take the interstate route is if you require nearly 100% cell phone coverage and have a large national carrier. I have Verizon Wireless (VZW), and in case you do too, on my route below I've noted the coverage for VZW to the best of my recollection. It's about 95% of the trip. Sorry, can't speak for other wireless carriers, but you should be able to research that.
Of the various routes we've taken, we like this one the best:
1. Wherever you are in DFW, navigate to TX 114 West (Carpenter Frwy.) out by DFW airport. Stay on 114 after it becomes Northwest Pkwy., all the way out past 35W to jct. US 287.
2. North on US 287 to I-40 West (Amarillo).
3. In Amarillo area, North on Loop 335 to North on US 87/US 287.
4. In Dumas, North on US 87 to the state line.
[VZW coverage is near 100% through TX]
1. Just stay on US 87 (aka US 64) to North on I-25. You'll be passing the Capulin Volcano, which is very interesting.
[VZW coverage is almost 100% through this route in NM, except near the CO state line).
1. North on I-25 to Denver area.
2. Bypass most of metro Denver - and most of the traffic - by taking CO 470 West (this is south of Denver) to I-70 West. But if you want to go through Denver, stay on I-25 to I-70 West. You'll be able to see the Front Range of the Rockies on much of I-25, and a good deal of I-70 has great scenery.
[VZW has nearly 100% coverage though this route in CO).
1. I-70 West. I suggest the shortcut in step 2 below, although you could stay on I-70 to I-15 North (I feel this is a waste of time, as Lmejh stated).
2. At exit 157, North on US 6 to the Spanish Lake/Provo area, then North on I-15 to Salt Lake.
[small parts of US 6 have no coverage on VZW].
Have a safe trip. I'm sure you'll enjoy the many areas of spectacular scenery Utah has to offer!