Ah, should be pretty easy then. The main thing to worry about is the filter- as soon as you switch it off, the good bacteria will start to die, so you need to have it switched off for as short a time as possible.
I'd try and save around 50% of the water if you can. You can get large water containers in aquatic stores or you could just get a couple of those cheapy folding jobbies that people take camping. Then get another container with a lid and put a bit more water in there, along with the filter sponge and an air stone hooked up to a battery-powered air pump.
The fish can just be transported in fish bags (local aquatic store or ebay). If you leave it until last thing so you can get it done as quickly as possible then that would be best. You can leave the gravel, decor etc in the tank but don't try to move it with any water in.
Then when you've got it all set up, get the original water in, top up with dechlorinated tap water and float the fish bags in there for a bit. You might want to test the pH of the new tap water just in case but if you're not going far then it should be similar.
We moved my 190litre corner tank recently to our new home without any fatalities or problems. We left all the fish in the tank with about 40litres of water but no ornaments or plants. So if we can do that you definitely can move a 60litre tank no problems.