Dear Olivier,
At the end of your analysis (or after you've reloaded a fit), you will have a tree with attached models to simulate from (call it myTree).
The function you want is
Simulate. You may need to tweak the characters option if your data is not nucleotides. Take a look at the documentation of the 'Simulate' command.
Code:characters = {{"A","C","G","T"}
{"1","","",""}};
DataSet sim = Simulate (myTree,eqf,characters,ancestralString);
ancestralString will be where you pass your root sequence, and
eqf is the vector of base frequencies (which won't be used if you pass an actual string as the 4th argument).
Cheers,
Sergei