Lea, I think you are asking two questions here so I will answer each.

Firstly, is she ready for solids? Well it is possible, only you know your child best. However, at just 4 months it is unlikely that her gastro-intestinal tract and system is sufficiently developed for solids. Barb has a written a fantastic post which I will have to hunt up and sticky, which outlines all the different reasons why GI systems can't sufficiently process food until around 6 months. The things you are describing do sound like normal 4 mo behaviour to me.

Secondly, if you do start solids now, can you use the Baby Led Solids method? BLS is suitable for use from when the baby is ready for food. So if she is ready for solids now, then yes. However, again, it is usually around the 6 month mark before they are ready.

HTH.