I am a divorced dad of a pre-school age child. His mother (who is not Israeli), wants to leave Israel with our child, permanently, to be near her family. Does she need my consent to do so?

Yes - or permission from the family court in Israel, if you do not consent. If your 'ex' relocates overseas without your consent or court permission, unilaterally, then this would be an act of civil child abduction.

If you oppose the idea of your 'ex' relocating overseas permanently with your child, then she must apply to the family court for permission to relocate, and you can oppose the application. If you have grounds to suspect that she is planning to relocate, unilaterally, because she knows you will not consent, then there are pre-emptive emergency legal steps that you can take, to prevent the child's exit from Israel.

Abduction From Israel