You don't need to fit a new cassette if a new chain works with the old one, and, even if you measure things, you can't be sure of that until you actually try a new chain. I reckon it's a 50/50 chance after 1800 miles.
Fit the chain and go for a ride, testing all the gears. Be gentle at first in case the chain skips. If there's just a tiny little blip occasionally, you might be alright after you've run in the chain for 50-100 miles. Any more serious problem and you'll need a new cassette.
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