Thanks for all the suggestions folks! In the end we gave up on the double stroller idea and got a Maclaren Vogue, which she is quite comfy in (will happily sleep in it), has a simple packup/setup mechanism, and is light enough for me to lift in and out of the car and on and off trains by myself.
Though if I'm just going for a short walk to the shops etc I will put her in the ring sling instead - she goes to sleep in a couple of minutes, and it's been a good way to make sure she's warm enough in the bitter Melbourne winter weather!