No, I do not believe that the 2008 presidential election was the beginning of a new party system in the US. There are two reasons for this.
First, there is not that much difference between the new coalition of Democrats and the old. The Democratic Party is still the party of the vast majority of racial minorities. It is still the party of unions. The Republicans are still the party of the religious right. They are still the party of the South. None of this has changed, making it hard to say that a new party system has arisen.
Second, it is not at all clear that we are entering a time of Democratic domination. The situation may well be more of a tossup with the parties exchanging power frequently. There is too much up in the air right now (such as how well the Republicans will be able to do with appealing to Hispanic voters) to be able to say for certain that a new party system has come into being.