There's nothing in Great Expectations that would suggest that Ms. Havisham would be interested in speed at all: as far as I remember, we only ever see her inside Satis House, wearing her wedding-dress, living in darkness. The closest we get to seeing Ms. Havisham at speed is when Pip is instructed to walk her around her dining table in Chapter 11 of Great Expectations, but even that isn't very fast:
She looked all round the room in a glaring manner, and then said, leaning on me while her hand twitched my shoulder, "Come, come, come! Walk me, walk me!"
I made out from this, that the work I had to do, was to walk Miss Havisham round and round the room. Accordingly, I started at once, and she leaned upon my shoulder, and we went away at a pace that might have been an imitation (founded on my first impulse under that roof) of Mr. Pumblechook's chaise-cart.
She was not physically strong, and after a little time said, "Slower!" Still, we went at an impatient fitful speed, and as we went, she twitched the hand upon my shoulder, and worked her mouth, and led me to believe that we were going fast because her thoughts went fast. After a while she said, "Call Estella!" so I went out on the landing and roared that name as I had done on the previous occasion. When her light appeared, I returned to Miss Havisham, and we started away again round and round the room.
I suspect that you're right that it's meant to be funny because it's unexpected: Ms. Havisham the ex-shut-in who's now become a daredevil and grown a need for speed, and is now a Cool Old Lady. This also fits in with her character in Thursday Next, where she's generally a superspy, pulling off impossible feats to save the day. In this regard, she's a bit like Granny Puckett from Hoodwinked, who turns out to be a little bit more active than you'd expect from Red Riding Hood's Grandmother (who we only see in bed in the fairy tale!).
Just 'cos you bring him up, it is perfectly in character for Mr. Toad to be obsessed with motor-cars (and to be vary of police attention).