The hill upward is very steep so if you go by car to a certain distance and just walk a bit with the stroller it is ok but all the way it might be very tiring.

Auf den Kahlenberg kommt man am besten, wenn man am Schottenor die Treppe runter fährt, in die Strassenbahn 38 nach Grinzing einsteigt, dort aus dem Torbogen zurück geht, über die Straße, in den Bus 38a einsteigt, hinauf auf den Kobenzl seine Runde dreht und weiter im Bus bleibt, bishinauf zum Kahlenberg.

No issue if you go by bus up to the hill. If you go by D Tram to the foot of the hill in Nussdorf, I recommend a stroller for the almost 300 highmeter up.

My advice is to take the 38A bus right to the top. There is a café with panoramic views over the Vienna and the Vienna woods. Take the path below the hotel, which will take you down through vineyards and into a village called Nussdorf, where there are cafés, and a restaurant/heurige called Schübel-Auer which is excellent for food. The walk is about two miles, downhill all the way. From Nussdorf you can get the D tram all the way back into Vienna. Its other terminus is the new Main Station (Hauptbahnhof).

The Kahlenberg is fairly flat at the top. The 38A bus goes there, you can pick it up at Grinzing, which is reached from the Schottentor by the 38 tram. Most tram routes now include low-floor trams, I am sure the tourist office or Vienna Tram Company can advise you further. They have a website available in English.