A few questions:
Is this a hobby project or are you hoping to build and sell many units? If it's a hobby project, are you doing it primarily to learn about building hardware? Or do you want this information so much that you'd be willing to buy some product that would do it for you? (eg http://www.surprisinggift.com/GPS-Tracker-Locator-Portable-G...)
Can you constrain the problem? Can you assume the cat is inside your house and you want to know which room it's in? Or is this lowjack for lost pets that wander away from their homes?
Getting a fix on the pet's position is probably the most challenging part. Transmitting information from pet to the web is easier.
You may want to look at the snif tag as an example of pet activity monitoring. It is like fitbit for dogs (or cats). http://www.sniftag.com/