In my 1996 Avalon, I've driven 60 miles before a fillup after the gas light has come on, signaling about 3+ gallons left in the tank.
Though I belive in the 2000+ Avalons the fuel tank is reduced from 18.5 gallons to 17 or something crazy. Otherwise I noticed the light pops on and I'll fill it with 14-15 gallons.
I couldn't imangine the light coming on with 10 miles left, the safest bet is to assume you have one gallon left when the light strikes.
Though, when the light comes on you should fill it, as mentioned heat problems, and too keep in mind that streching the time between fillups does not use any less gas, you still drive the same distance!

(well, sure the added weight may decrease mpg, but you'll always have gas to go somewhere!)