Unless there's something they haven't talked about yet in the show, there's not a reason for Baelish to kill off Robin Arryn.
Baelish is now the Lord Protector of the Vale until Robin comes of age, so he's in control for the forseeable future.
The assumption is that the north will rally around the Starks when the time comes, so as long as he holds on to Sansa, he'd have control over Winterfell as well.
He has control of 2/7 kingdoms now (Harrenhall, the Eyrie), with eventual plans on the third (Winterfell). He's got to be playing the long game, but I can't see what he would go for after Winterfell, maybe Riverrun?