It sounds as though you want to move everything across and just have the 180, not run both tanks?
The process is quite easy, but with a newly cycled filter you'll have to be a bit more vigilant. The filter bacteria live in biofilm and this takes a few months to fully develop. Until then, the bacteria colonies are more delicate. You will need to be careful during the transfer and monitor your water more closely afterwards compared to when I upgraded a 10 year old tank.
You have two options regarding the filter. Either take the media out of the old filter and put it into the new one, or run both filters together for at least 6 weeks. The first is preferable as with the latter the bacteria will spread out between the two filters in proportion to the amount of media; then when you remove the old one, you'll lose some bacteria. If the 180 has the same type of filter as my Rio 125 had, replace the carbon sponge with the old media and if there is still some old left, replace another sponge (green if they still use it). Don't remove the blue sponges or the cirax if that's included.
If the 180 is going in a different place you can take your time. Set up the new tank (check for leaks somewhere else first if that sort of thing worries you). Fill it with dechlorinated water and let it run to make sure the heater and filter work properly. Don't put anything in the tank just yet.
On transfer day, turn off the old tank, remove a bucketful of water and put the fish in it. Cover the bucket (a towel will do) as stressed fish can and do jump. If the filter will fit, put it in the bucket too. And the mossballs and bogwood/java fern, though you might need a second bucket for those.
Remove some water from the 180, slightly less than the amount in the 64 litre and replace it with as much water as you can get out of the 64l without distubing any muck in the gravel. Take out the gravel, wash it, put it in the 180 and add more to get the amount you want. Now move the filter, or put the old media in the new filter. It is fine to cut sponges up to make them fit, but keep everything wet. Put your decor in the new tank and if you use second bucket for the plants put the water in the 180 as well.
Strictly speaking, you should acclimate your fish as if you'd just bought them. But you have been doing lots of water changes with the fish-in cycle so your water won't be very different from your tap water. And about a third of the new tank's water is from the old tank so it's like doing a 65% water change. The main danger will be if the bucket has cooled down so the tank is a lot warmer. Maybe put the old heater in the bucket and switch it on to prevent this. Net the fish out of the bucket and add the water to the 180.
If the 180 is going in the same place as the 64l, it's a bit more complicated. You'll find a brand new dustbin will hold the water from the 64 litre (more expense I'm afraid!). Empty as much clean water as you can into a bin. Half way through, transfer the fish, plants, heater and filter. Move the bin out of the way and plug in the heater and filter. Then empty the 64 litre, move it and put the new tank in position. Fill it up, switch the filter and heater on and wait till the water is warm. If you fill with warm water it shouldn't take long. While it is warming, you can be sorting out the gravel and adding any non-plant decor. Then turn the electrics off, remove some water and continue the transfer as above. Transfer the fish when you can catch them easily.
Wait at least a month before getting more fish. This will make sure the new tank has settled and the filter has recovered.
Using warm water to fill the new tank -
If you have a combi boiler, it is safe to use the hot water tap. But if your water is stored in a hot water cylinder, you'll need to boil a kettle. This type of hot water system fills the cylinder from a cold tank in the attic, and all sorts of nasty things can find their way into that; things you don't want in your tank.