Redeye autocorrection often doesn't work.  Have your kid show you how to do this with Photoshop or some other photoeditor.

Magnify it until the eyeball fills the screen.  

With the Paint tool (choose an appropriate size), paint out the redeye ("greeneye" in this example).

Note how I preserved the original white reflection.

Alternatively, you can paste a big black dot over the pupil, and then draw in your own white fake reflection, but I think that's more work.

Photoshop prompts you to save it as a .psd file (which is huge).  If it's just a snapshot, I skip that and just save it as a .jpg file.

This is crude, but corgis aren't fussy.

Shoot without flash by ambient light at high ISO speed, and you won't have redeye anyway.