Trying baby-led weaning, but for a baby who puts everything in her mouth (toys, my hair, etc), she just plays with the food and doesn't eat it! Should I just try the conventional way of feeding her?

It is okay. Just place the food in front of your baby and show baby how to put into mouth and eat. You might need to repeat for few times or over a few days until she gets the concept of eating. It takes time and patience. BLW is fun. You try to observe for few more days and don't need to offer puree first.