Am planning to tow a light trailer several thousand miles. Total weight will be 1000 pounds or less. Advice?

Bought an '05 Vibe in May and really like it. Once about a month ago and again last evening, I got in to start it, AC running and the fan speed nearly full and it never turned over before the whole electrical system shut down. The first time it happened, power came back after 15 to 20 minutes. Last ...