You'll be fine. A long x-country over such varied terrain as you propose, is one of the most valuable trips one can take for learning purposes. Nothing beats real world decision making. I've done quite a few of similar length in my old twin VFR, and they've all been very educational.
Just make sure you have plenty of time, don't push your luck and know when to give up for the day or for a few hours. Also, crossing the Rockies (which you'll have to do) is a high altitude endeavour and should be respected. If you don't feel comfortable with 12000ft crossings or higher, then your only option is to do it very close to the Mexican border through Arizona and New Mexico. There you can squeeze by at around 9500ft if the weather cooperates. On the other hand, you're flying over very uninhabited states there, so you're on your own for long periods of time - no radar coverage and frequent lost com with controllers etc.
Here's one of my trips from last year where I encountered terrible weather and had to stop numerous times!