In a 10- to 12-inch nonstick frying pan over medium heat, frequently stir pecans until lightly toasted, 4 to 5 minutes; pour into a small bowl.
In the same pan over high heat, shake and tilt sugar often until melted and amber-colored, about 3 minutes; take care not to scorch.
Remove from heat and add whipping cream and rum (mixture foams). Return pan to medium heat and stir until caramel is dissolved and smooth; boil vigorously, stirring occasionally, until mixture thickly coats a spoon, about 10 minutes.
Pour into a 1 1/2- to 2-cup ceramic fondue pan, other heavy metal pan, or metal chafing dish in a water bath jacket. Set over a votive candle or ignited alcohol or canned solid-fuel flame. Adjust heat to lowest setting under fondue pan, to medium under chafing dish.
Spear fruit or cake, 1 piece at a time, on fondue forks or thin skewers (metal or wood) and swirl through dulce de leche fondue (stir across bottom frequently to prevent scorching), lift out, and let drip briefly over pan. Sprinkle bites with a few nuts, as desired.
This was fantastic eating, and once I managed not to scorch/scald the sugar (twice!), "easy" to make. Here's what worked for on my successful third attempt: put sugar in pan (over *medium/medium-high heat, not high as the recipe calls for) until it liquefies, stirring with a whisk constantly. As *soon* as it liquefies, remove from flame immediately, so as not to scorch it (it will continue cooking/browning even off the heat), and, while the melted sugar is off the flame, stir in 1 c. heavy cream and the rum (or other liquor). Return to burner over low heat and simmer a few min. (didn't need 10 min. as called for, closer to 5). (Also, if you have a gas burner as I do, I found that I needed to use the lower power/simmer burner!).