Is it OK to let my six months old kid get close to my guitar?

I see that she likes when I play on my classical guitar. Mostly she sits and looks but sometimes she tries to reach it and play with strings. When this happens, I push her back because I still remember how ten~ years ago one string snapped and almost hit me and I'm afraid it will happen again and the string will hit and hurt my kid. Please tell me, am I paranoid or not? Do you let your kids close to your instruments?