i would place a hot water bottle under the nest (outside cage) to dry and dry the nest out a bit and keep it warm.

the babies are only a day old and its extremly risky to move them at that age, especially when the mum isnt really use to you yet either.

i would also place some new dry bedding in the cage and hope she moves the nest.

if you wish to risk moving them all then take the chance but personally i wouldnt at this age.

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animals are my life

i have:
2x dogs (rottweiler and a jug),
1x african grey parrot,
2x rosella parekeets
4x syrian hamsters (baby, mocha (wiggy), peaches and daisey),
2x winter white dwarfs (sunshine and harry),
1x female leaf insects (doesn't have a names),
1x female corn snake (awaiting eggs),