You probably want to look into suppliers for copter drone parts - the kind that RC hobbyists attach to drones or RC cars to fly/drive from a first-person point of view. These are called FPV ("First Person View") cameras. They're already designed to be light, compact, and battery powered.
I don't want to be partial to any brand or model, so I suggest you search for RC FPV cameras and/or drone fpv cameras yourself. See also "What should I look for when choosing a FPV camera" in the drones.stackexchange.com site.
For the full setup you'll need:
- A camera. These typically output analog composite video.
- A video transmitter. These input composite video, and convert it into radio waves.
- A battery, to power the camera and the transmitter.
- A video receiver. These take the radio waves and output composite video.
- A way to watch the composite video, either
- An analog TV monitor with composite input, or
- A computer with a composite video capture card (which can take the form of a PCI/PCIe card, or a USB dongle), or
- A specialized unit (RC receiver, VR glasses)
The camera+transmitter and the receiver+capturer might be in the same package (read "inside the same plastic box", sold together as one unit), but you should be aware of all the system components. If your goal is to provide video in a website dashboard, you probably want the video capture card and the webserver in the same computer (I'd recommend motion for the software bit, since I've used it in some raspberry-pi projects).
I'm afraid any further detail would be off-topic for bricks.stackexchange.