The approximate measurement should be sufficient information to go on provided the motor has some form of belt tension adjustment that can take up a limited amount of slack.
If you were of a mind you could add an idler wheel that could take up 'any' amount of slack.
Searching eBay using 'tumble drier belt' shows thousands of results, many of which have numerical designations that INCLUDE this one:
https://www.ebay.co.uk/itm/TUMBLE-D...hash=item2c53380d21:m:m3Wphv5I8gvRYkPT5_JwYJQ
which, conveniently, is 1920mm and (presumably) 9mm wide......
If you also add '1920' to your search word you will find many others - seems like 1920mm is a standard size so maybe your measurement technique is pretty good!
The WIDTH of the belt will depend on the torque it's under but a 6kg load is at the very small end of the scale so even 10mm width would seem to be on the generous side.