If it's not fast enough, you're not paying attention to trends. There's tons of modded electric Powerwheels/Barbie Jeeps on Youtube with upgraded motors (and upgraded batteries too for longer run times). There's a kid that drives a modded-out Lightning McQueen car that is at least 10X faster than stock.
On the gas kart, I wouldn't attempt adjustable pedals per se, but just mount a separate pair of pedals close to where she can reach them now with her legs bent. For example, drill two longitudinal holes in the frame for the gas and brake pedal to where the driver can reach them now and connect them to the main (adult) pedals with threaded link rods. So, two gas pedals same distance apart, linked, and the same for the brake pedal.
I say place them at a fixed distance because average height adults think the most karts are
too small because they think they should be able to stretch their legs out straight, no bends, but you're supposed to assume the crouch/squat position to ride these things.
The photo in post #8 is basically what I mean:
https://www.diygokarts.com/community/threads/i-cant-reach-my-pedals.32283/
EDIT: Or anderkart's photo in post #23.