If there's no time to cycle the new tank properly then make sure you're keeping a strict eye on water parameters - mainly Ammonia and Nitrite.
Doing regular water changes (2 - 3 times a week approx 20%) while the new tank cycles, to avoid any build up of toxic substances.
You can use the water from the old tank, but bear in mind that hardly any / no beneficial bacteria lives in the actual water, it is actually on the tank glass / filter media / any solid ornaments or plants, so it's also a good idea to put them in the new tank :happy: