Axolotl are an interesting choice because they have a very weird evolutionary history. Axolotl are actually evolved from more land-living amphibious salamanders by neotony, that is they evolved by the immature - and purely aquatic stage - of an amphibious organism becoming sexually mature. For an axolotl to become amphibious is therefore very easy, it's actually possible to artificially induce metamorphosis to a salamander like state and thus the pathways necessary still exist and just need the right conditions to favour them for evolution to do the rest.
The rest of it is not that dissimilar to real evolutionary history, which is far too long and complicated to do justice to in a single Stack Exchange answer, but in super-duper tldr; mode: first you need to evolve to be properly land-living: i.e. evolve proper lungs, skin that can cope with being dry, and eggs that can be laid on land. Then you need to evolve proper quadrupedal stance, so the legs are orientated under the body, rather than to the side as in most lizards and amphibians. Finally, you need a situation which favour bipedalism. It's not really clear what exactly this is: it's evolved in various dinosaurs (including birds), kangaroos, and humans.
Incidentally, beaver-sized Axolotl are likely not biologically plausible due to the requirements for respiration which since the surface area of their skin and gills increase with the square of their size, won't scale sufficiently to match their increase in volume.
Also, thousands of years is super-duper ultra-quick in evolutionary terms: whilst significant change can occur on these timescales during adaptive radiations, it's far more credible for the kind of changes you discuss to take place over tens, or hundreds, of millions of years.