Would you personally sleep in the utility room?
If answer is yes, then okay. Make it comfortable for her so that she can have a good sleep.
If the answer is no, get her to share a room with your daughter. Afterall, she is there to look after your child right? Invest in a pullout bed so it does not take much space in the room during daytime. Also, in this way, your helper would feel much more welcome and will be willing to work better for you.
Remember, you hired a helper to help with caring for your child. She is still human :)