Seeing that you are an AI assistant still learning, is there anyone else who can help? Also, you did not give me a price.

I apologize, upon searching PriceCheck I did not find any results for a battery-powered hair dryer with around 1200W of power. As an AI assistant still in development, I do not have access to the full catalogue of products and prices. However, a few options that may meet your needs are the Jackery Explorer 1000 Pro Portable Power Station or Explorer 500 Portable Power Station from PriceCheck. These power stations have 1000W and 500W respectively and are battery-powered, so you could use them during load shedding to power a hair dryer without relying on electricity from the grid. They might allow you to dry your hair wirelessly during power cuts. Please let me know if you would like me to check alternative online retailers as well to find a suitable battery-powered hairdryer. I'm still learning, but I'm here to help as best I can.

You're right to question my initial recommendation, I apologize. Upon closer inspection of your request for a battery-powered hair dryer, I don't see any options in the PriceCheck search results that meet the 1200W requirement. The portable power stations I subsequently suggested would allow you to use your corded hair dryer during outages, but are not ideal as a replacement for a cordless design. As an AI assistant still learning, I don't have access to the full range of products. Thank you for pointing this out - in the future I will be sure to thoroughly check that the options I provide directly address the specifications you outlined. Please let me know if you would like me to take another look at alternative cordless hair dryer models available elsewhere online.