You wouldn't get root rot unless you overwatered,
You could easily go from a solo cup to a 5 gallon, I went from a 4in black pot, which is about the size of a solo cup, To a 10 gallon rubbermaid tub and i've had no issues. Water very very good when you transplant her and lift it to see how much it weights, then keep checking every other day or daily and when its light, water.
I'll admit im a fairly new grower but in my 4 years of growing and 2 working at a nursery i've never heard of getting root rot from anything but the roots literally sitting in stale water. Could be wrong, Anyways watch your watering and you'll be fine. Just my .02 Happy growing, Good luck, Stay high!
EDIT: Also i'd wait atleast 2-3 weeks before transplanting it, The stronger the roots are the less likely soil will break off while transplanting and cause major shock.