Great question. We normally look towards the winter season for the most consistent impacts on the Jet Stream across North America as that is when La Nina's tend to peak. However, there could be impacts during late fall as well. The difficult part is parsing out what is influencing what! 
Of course, even having a La NIna doesn't mean that the jet stream stays in one shape an entire season. So that's where the importance of shorter term forecasts come into play.