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Some people do let the ham have some playtime in the new cage but I never have, it won't have all Tofu's things & substrate in anyway so I'm not sure it really helps.
The most important thing is not to clean for at least a couple of weeks before the move if possible & at least a few weeks after (except for spot cleaning pee( so everything keeps her scent on it.
I would put as much of the new substrate as you need in the base of the cage allowing space for all the substrate from the old cage on top or at least a fair amount of it.
Don't clean any toys, wheel etc either for a good while.
If you can make the layout similar that might help too.
It might take a little while for Tofu to adjust but she should be fine soon enough, it can be tempting to move things or change things if they don't seem to settle straight away but it's best to just leave them to it unless something really isn't working.

ETA I forgot to say if you can transfer her nest over as well, if she has a food hoard then you could transfer that to a similar place in the new cage too.