I wouldn’t. The purpose is to give you eyes to see your child when you’re away from them. I wouldn’t tell her to be sure she’s giving you quality care.
On the legal side of protecting yourself from any backlash of recording your sitter, use a contract. You should have one in place especially if your sitter will be keeping your child for a specified amount of time. In the contract make it clear you may use cameras and recording devices.
Cameras will not only give you peace of mind but it will help you navigate should you need to. Cameras have aided many parents over the last few years be an advocate for their children when they aren’t around. Cameras can be purchased at stores should as Best Buy, Target, etc. They also now come with many security systems.
Don’t tell your care giver where they are but utilize them in places where your child will be. Hopefully you won’t have to use them in any criminal prosecution. Your child is precious and in this day and age you need them even with the most trusted adult.
Congrats on your new baby. Go back to work with peace of mind and some visual back up.