So let's look into it.
To be perfectly honest, I was reading this word wrong, which may account to some degree for my inability to make sense of it. I kept seeing it as "laudaulet", and in fact the header originally said that, but I decided not to perpetuate my own confusion.
Well, I guess you could say that the landaulet was an Austen era convertible. It was a smaller version of the landau, named for the German city in which it was manufactured, which was a light four-wheeled carriage, suspended on elliptical springs, whatever those are. (Although there is a minority theory which has it that it all goes back to the Spanish lando, a light carriage drawn by mules, and going back from there to the Arabic al-andul.) At any rate, the landau has a two part folding top that comes from the front and the rear, while the landaulet only has the the rear folding top.
If you're wondering why P.D. James bothered specifying such a vehicle in the story, because I certainly did, well, it turns out that there is a lot of differentiation between carriages in Austen's novels. In fact, here is a very lively little paper on these things, which for Austen fans is much more worth your while than anything further I could say here.