Two-Year-Olds and Turntables...

Call Dr. Laura. I will save you the call and say that you have failed in parenting. When I was a child NO meant NO!!! A cattle prod might just be the trick though. Maybe a barbed wire or small electric fence might work also.

Fortunately my kids are old enough that they know that to touch my stereo guarantees a serious readjustment of their VTF (especially when they later try to sit).
If I had a baby or toddler to worry about, I'd put something big and/or heavy on top of a tablecloth on top of the tt. Out of sight, out of mind, out of harm's way.
Uru, kudos for bucking the pc trend. In my experience however, even the best-behaved kids are prone to accidents or unprecedented dares. With a deep-four-figure cartridge that no child would recognize as pricey and frangible, for my own peace of mind I'd opt for removing (disguising) the temptation.
Save the cattle prods for cable burn-in, amigos!!
cheers apo

if you do not have access to a man cave, a very tall chest of drawers/dresser works fine.

It's simple.Play a record for the child. Then a CD of the same recording. She will gain an immediate respect for the turntable and leave it alone.

I sounds like you already have plenty of good advice, but I'll weigh in anyway. I subscribe first to Albert Porter's approach. In my case, my audio was in a room that was off limits,and my kids surprisingly behaved.

On the other hand, I'm a little surprised to hear you say you prefer your table low. I mount mine at chest height. I really don't like bending over to position records. Were it me, I'd move it to a higher, sturdy location - possibly wall mounted as Dave suggests.