They could do it, but I seriously don't think it would do anything positive for them.
Brook Lopez is such a slow, immobile lump of a guy that they really kinda NEED a more athletic and defensively capable power forward like Thad Young playing alongside him. The two actually complement each other very well.
Trade Young for Jennings and they solve their PG problem, but then they create one big new problem at PF.
This is the problem with the whole Brooklyn roster - they simply don't have enough talent. They only have two good players on the team (three passable ones, once you add in Johnson) and there is only so many ways you can arrange three players into 5 starting spots. It really doesn't matter who they trade to fill up a hole, they will be creating a new hole somewhere else.
They can consolodate by trading multiple bench players for a solid starter either, because their bench players are all hot garbage.
Nor can they trade picks for a solid starter, because they pretty much don't have any picks.
Really, the only way Brooklyn can possibly improve from here is via free agency, since they should only have about $45M - $50M committed next year once Joe Johnson's contract expires and theoretically should be in a solid position to add one or two more guys that way.
Really, there's no point in Brooklyn doing any moves right now. Even trading away Joe Johnson for cap relief is pointless, because they could just let him expire after the season (lets be honest, this season is already lost).
Unless they want to try to trade Young and Lopez away for picks or young prospects, the best move for them to make right now is no move. Their best hope is to build around Young and Lopez as their core, and try to add a start and a few nice support players to that core.
Honestly, the Eastern conference is pretty wide open right now. If Brooklyn are smart (and lucky) in free agency and add the right pieces to that core, they could very seriously have a shot at competing for a playoff spot next year. If I were the Nets, that is the direction I would take.