Nice!
It's always fun to make and use setups like that.
While 'hard-wired' is definitely the cheapest / quickest setup, 'wireless' is definitely a more versatile option..
You can use it indoors - hard wired power via a power supply / wall-wart, or use batteries..
And then if you want to go mobile, batteries or even some usb power-banks will do..
I've done tons of wireless audio/video setups over the years, and a Very Common place to start is:
Search for: "Wireless FPV Cam Kit / Setup".
In the RC Flying Hobby, this is what we use - to see what the aircraft sees.
[We usually send the video feed from the craft to our video goggles - other times, monitors are used]
[More expensive and in depth, but the possibilities for use is endless]
Needed:
CAMERA - with video output. [can be solder pads or auxiliary jack style]
*We typically use CCD cams that look like a little circuit board w/ an attached lens.
[Usually fixed / fisheye view] Better / Different camera setup can definitely be used - Especially for this..
WIRELESS A/V TRANSMITTER [VTX] - The camera hooks to the transmitter. It sends video footage OUT.
WIRELESS A/V RECEIVER [VRX] - The receiver brings the video footage IN - and attaches to a viewing source:
Viewing Source - This can be a TV, Computer monitor, Dedicated monitor - like security cam screen, Video Goggles, etc.
The camera and the transmitter will have to be powered [together] - 5v is great. Low power consumption / most usb battery banks can power them, etc.
Some go 5v, 12v, [dual voltage for power is best yet but not necessary]
The receiver / viewing source will have to be powered [together] THIS is where Dedicated monitors are usually best..
FPV Monitors [like the back-up cam monitor in a car] are typically used..
FPV Monitors will range in quality and price depending on resolution, etc.
They're usually 7.4v dc up to 12v dc [We usually power them with a 3-cell LiPo battery - roughly 12v]
The VTX [Video Transmitter] and the VRX [Video Receiver] have to 'communicate'
Both the VTX and VRX will have 'dip-switches' and/or a button and screen to match and sync their 'channels'.
When the frequencies sync, you'll have video. Different channels / Different broadcast strengths offered too.
They'll also be fitted with some type of antenna..
Usually just a little wire, or a cheaper 'dipole' antenna.
For better/farther range, we use custom antennas known as Cloverleaf - 3 lobe and Skew Planer - 4 lobes:
Cloverleaf 3 lobe for the Transmitter / Skew Planer 4 lobe for the Receiver.
They just offer a wider / more spherical radiation pattern, so they'll work better in more settings / positions etc..

Sam -