You do not need to cycle a new tank if you are willing to transfer the biofilter. The safest is to transfer all the substrate & decorations and the filter. But you can do that with just the filter alone if it is well seeded. <I.e., don't do this right after you change the filter pads.> If you are not reusing the substrate (gravel), you can put it in a mesh bag & put it in the new tank during the transfer, and remove it after a few weeks. <Generally, you only need the top half of the gravel.>
It is important to keep all the media wet in dechlorinated water during the transfer, and aerate the water if you are going to take a long time. If you are going to take more than a day, you would need to feed the biofilter either by running it in a temp tank with fish (as I suggested earlier), or add ammonia to the aerated water containing the biomedia.