Ive moved some gooseberry bushes early October over the years.
Certainly down here a gooseberry bush would be nowhere near dormant this time of year.
Pretty much the same as above. I add a mixture of homemade compost to the hole before planting.
Do water it in well and keep watering it a few times a week for its first month.
Do not feed gooseberries, just mulch well over winter with homemade compost and of course do not forget late autumn and early winter to prune well.
Also, as mentioned above, take some cuttings from the plant before lifting as they will be fine to grow on this time of year. I have in the past planted my cuttings in old buckets, making them easier to transplant on after a year. Do not prune too harshly first year in their final position, they start producing first year but will produce best their second year, when you prune well.