Would you rehome your dog if it bit your child?

I have a 5 year old Australian cattle dog with some anxiety issues. She gets spooked really easily. I have a 2 year old and an 8 month old. She generally keeps to herself. The other day my 2 year old was walking into the kitchen and he tripped over a toy and he fell on the dog. She bit him in the face and drew blood. It was pretty bad. Everyone is telling me to get rid of her. She has snapped at him before for getting too close to her but has never chomped down like that.

Would you rehome her? If I separate them then she’s going to have to be outside or in another room by herself all day because we do not have a large home.