I deal with similar requests all day at work, and the simple answer is that with current technology it's very difficult to offer a live video stream on a domestic broadband connection.
A live (25fps) VGA video using H264 compression (same as Blu-ray and fairly standard for CCTV) will give you a very good clear image, but will use around 500kbps of bandwidth, which is higher than the upload bandwidth of most ADSL connections. Dropping the frame rate will help, but will provide a very jerky image.
What we normally recommend for people who want to show building sites or weather conditions is to set a camera to drop an image onto a webpage every 15 minutes or so, but your situation is different.
What I would recommend is to produce a short film clip for each kitten and upload them separately with a thumbnail image so visitors can see each cat in "real life" so to speak.