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?

Sounds like my son. I first tried feeding my son puree with a spoon and he keeps trying to grab the spoon instead to self feed himself. He ends up gagging because he puts the spoon far too in his throat. After a while, I ended up doing semi BLW with my son. It's messier, he plays with it but he does eat it. It's not important that he eats most of it as his main nutrients are still coming from his milk. But it's a good way for him to experiment with different variety foods, textures and taste. I use a high chair from Ikea which is pretty cheap, approx. $30 in total and I'd leave steamed fruits or vegetables on his tray. Now that it's been 2 weeks, he knows that it's food but once he's done from it, he'll throw the food about. Don't give up mummy. Your baby will figure it out soon