Given the way most banks are completely flummoxed when you try and activate a PoA, I would not bother to tell the bank.
However, giving a PoA to one person only is rather offering hostages to fortune. What if, for any reason, your daughter is ill or for any other reason, cannot take control of your affaits when required?
It is usual to give a PoA jointly to two or three people, with the instruction that they can act together or separately. That way, if one is unable to act, then someone else can, and with two people holding it, someone is always likely to be able to act when the need arises and both will have their own copies of the PoA.
My parents included all three children on their PoA and both of our children are included on our PoAs.