When to Replace a Cassette

If you have only worn one chain from new to 0.75 wear there is no way the cassette is worn out. The chainring will wear out first because there are relatively fewer ring options for the chain to be on, albeit over a bigger arc......the chainring may wear round 1.5 (0.75 x 2) chain equivalent and the cassette 2-3 (0.75 x 4) unless you bought a super expensive lightweight cassette which do wear a bit faster.

Post close-up photos of the cassette teeths. The photos will tell us if "small lip" is small don't worry about it the cassette has good life left, or it's worn and needs to be replaced.

Tuggles is spot on. Chuck the new chain on and ride it and if it skips, change the cassette as well. My winter bike spends it's life with chain and 105 cassette covered in liquid, gritty mud and the cassette is still good at ~2,500 miles.

You would soon find out if you put a new chain on the bike.  If the cassette was too badly worn a new chain would not mesh with it and you would get jumping, expecially when you put pressure on the pedals like going up hill.

It doesn't sound like that much mileage for the cassette to be worn out, but riding with a badly worn chain will drastically reduce its life.

Would sound like to me the chain and cassette would need changing, if it is streached by that much.  How are the chain rings?