Can I use my Mac keyboard as input to another Apple device?

Any of these three apps turn your Mac into a Bluetooth keyboard, and should accomplish what you need:

• Typeeto
• Type2Phone
• Mocha Keyboard

1Keyboard is an OS X app that allows a Macintosh keyboard to type on another Mac, iOS devices like iPhone and iPad, Apple TV, PS3 and Android.

I followed the pairing instructions, and while it didn't work the first few tries, it does now. Once I got it up and running, it has worked just fine. Copying, Pasting, keyboard shortcuts and Media keys (Volume, Playback) are supported.

You can set keyboard commands to connect to different devices. I use Shift + ⌘ + > to connect to my iMac, Shift + Ctrl + > to connect to my iPhone, Shift + Alt + > to connect to my iPad.

I am not sure about its compatibility with El Capitan but Teleport will let you do exactly what you want. I used it for years to connect one keyboard and mouse between 3 Macs, but have not used it in awhile.

Try Synergy, a software KVM: https://symless.com/synergy

This allows you to simply move your mouse pointer to the iMac's screen to control it. Move your mouse back to the MBP and now you're controlling it. You can also do useful things like share clipboards between the machines.