I have a few questions...Did you give up going to work part time some where else to stay home and babysit for this friend? If so, then I would talk with her and explain that you agreed to the oral contract based on you getting a weekly paycheck regardless of you watching her child or not.
If you never had intention of working outside the home and stay home regardless and you did not have to make any special considerations for the child not being at your home, then I would let it go. i personally couldn't take money for not having performed some type of service.
Now I would feel differently if the child was missing a day during the week for being sick etc... Cause then you were planning on the child being with you and thus you didn't make plans for yourself in lieu of babysitting, so she should have to pay if though you didn't provide a service per se, the planning of providing the service prevented you from enjoying the day as you normally would. So the money would be compenstaion for your inconveinance.
I don't see the week of vacation as that though cause they had to have told you they were going to be gone that week and thus you could make plans for the week as you normally would. unless they informed you that Monday morning, then I would want pay for that day at least.
I would want some type of notice so that your plans are not affected, but full pay for a whole week in your situation seems a bit much. Day cares get it because they are not able to make other plans if your child doesn't show....they care providers still have to be there regardless and the fees they charge for a full class is how they cover their operating costs, but since you really don't have that, it is a different situation.
So unless her plans have prevented you from doing things you normally would, I don't think you are entitled to compensation. My opinion and I would definately try and work up a written contract if you have any intentions of doing this long term. Perhaps negotiate terms regarding vacation, like a 5 day notice required for no compensation otherwise, if only 3 days notice, then 2 days of compensation will be given, etc.. Sick days are to be compensated regardless of notice. Parents are to provide any baby proofing items requested for the safety of their child and will be returned once no longer needed. State exactly what will happen in case of an emergency, such as you being taken ts o the hospital unexpectedly or if the child is for any reason taken. i would have the child's allergies documented, so there is no question as to wether or not you were aware of any. If you are asked to give medication at any time, I would require them to give you that notice in writing and not trust verbal. There are reasons that day care centers do this! Have they okayed you taking infant on errands around town with you? or do they ask that you not leave the premises? Have they given you permission to bathe the baby if say she gets covered in baby food once older, or do they ask that you only baby wipe her down? Do you have their permission to take the baby for a walk?
I know you trust these people cause you have known them a long time, but the relationship changes when money changes hands!!
What is to happen when you go on vacation? or are sick?
Oh & have you discussed taxes? will she be giving you a 1099 at the end of the year so she can write off child care monies?