X10.com, while it is an atrocious site (and a bit offensive also), has some really cheap deals on complete webcam packages.
This one comes with a wireless webcam, transceiver, pan-and-tilt webcam base, and software to allow remote monitoring all for $100. I don't really know much about all the components since I haven't used any, but it is an all-in-one solution that might be worth it just for the sake of simplicity.
To get through your work firewall you will need webcam software that can broadcast on common ports. You would need the software included in the above package to be able to be served on a port that will make it through your work's firewall. If it can, all you would need to do is leave your computer on, and then you wouldn't need any external hosting.
I have used a small mac application before called
evocam. It's only $30 and works with your webcam or built-in isight if you have an iMac. Just point the iMac at the room and run the software. It has a built-in web server so you can serve it right from your home iMac.
The easiest solution is most likely going to involve getting some simple webcam streaming software running on your home computer. Does the dog roam the house, or is there a kennel/room? One camera will certainly be easier to manage and get set up initially.