I did this exact thing, when my dd was an infant. I had a 10 year old girl come over to supervise and play with my son. I met with her and her mom and we established some basic ground rules (no cooking or microwaving, but there were appropriate snacks on a particular shelf (fruit cups, graham crackers, etc) that she could serve at a certain time, and there were some carrot sticks, etc, in a bowl in the fridge that she could serve (again, not unlimited, but at a designated time so as not to interfere with dinner). She played with him and helped him pick up his toys. She was not to just plunk down in front of the tv with him or play electronic games - the point was to have good old fashioned play time (creating a road for toy trucks, playing with Legos, play board games, etc). She supervised him washing his hands, things like that. I did not leave the home when she was there, but took a shower, sometimes lay down if the baby would stop crying for 2 seconds, took time to actually drink a cup of hot coffee and answer emails, things like that. She was responsible, and her mom thought it was a great way to train her to be a babysitter when she was old enough. I was glad that her mom was involved. I would not have been comfortable just making the arrangements with the young girl. I wanted her mom to know what I expected.
If your baby is happy, and in a safe baby seat or swing, and if the girl doesn't need to tend to the baby (just pick up the baby's rattle or toy, or wash the pacifier if it falls to the floor), I think that would be ok. But I wouldn't want her carrying the baby around or trying to give the baby a bottle.
I think one dollar per hour per child is reasonable to begin with. $2 if she's just playing with your older kids or helping them with homework or serving snacks or helping them pick up their rooms. $3 if the baby is in a very safe place and the girl just keeps an eye out and notifies you if the baby seems to need changing or feeding or burping or whatever.