Our cat is 10 months old and is her 63rd day of pregnancy today. She is not really showing signs of labour yet. As this is her first litter and ours too, we thought that they had them around 62 or 63 days. When would be time to worry and take her to the vets?

Take your cat to the vet today, her body is not fully developed at 10 months. SHe'll be lucky if she doesn't have major complications as well as her kittens. Here is some reading for you... there are other links on here that tells you of the health, behavioral and social benefits of spaying. Give it some thought. There are not enough homes for all the cats that are born each year, so that means a lot of them will be killed in the shelters or out roaming the streets.
Feline How-To Manual: Pregnancy and Delivery ~ Pawprints and Purrs, Inc. (http://www.sniksnak.com/cathealth/howto15.html)