Fermentation should take place at the recommended temperature for the yeast strain you are using. If it's not on the package, Google will help you find that optimal temperature. Keep in mind, that is the temp the wort should be at, NOT ambient (room) temp. And that should be for the first week or two of fermenting, not the last week or two.
How long? ultimately, it depends on what your hydrometer tells you. When you get the same reading for 3 successive readings (3 or more days) and they're below 1.20, then you're probably done. (1.1 or lower would be better, 1.2 is relatively sweet, but some kits seem to get 'stuck' there.)
SO - yes, it might be 'ready to bottle' in as little as a week. You will find that temperature control, sanitation, and patience will yield you your best beers - many of us leave our beers in the primary fermenter for 2 or 3, even 4 weeks - under temperature control, of course, and then bottle.
Many of us face the same problems as your south Texas location. ANY beer made in "room temp" in Texas, SC, AL, MS, LA, etc ....will be less than optimal if you don't start off with some temp control.
Inexpensive options include a tub filled with cool water, with some frozen water bottles added as needed. That usually requires one or two exchanges per day, but can make some decent beers.
good luck, welcome to the hobby and HBT!
