Can I charge tax on the shipping fee as well?

Yes. Go to Settings → Store Settings → Manage Tax, click Tax Settings, tick Charge tax on shipping and click Save Settings.

When it's on, the order's shipping charge is added to the product subtotal before the tax rate is applied, so one tax line covers both. When it's off (the default), only the products are taxed.

Points to note:

• It uses the same rate(s) as the products. You can't set a separate rate just for shipping.
• If shipping is free (a free-shipping threshold, free-shipping coupon or store pickup), there's nothing extra to tax.
• It also works with Product prices already include tax (inclusive). In that case the tax is treated as already inside the shipping fee too.

Check a test order to confirm the tax line looks right.