Grandmother stressed while 17 month old grand daughter sleeps over

I am a grandmother for the first time and simply adore my little granddaughter who is now 17 months. My problem is that I am very nervous when she sleeps overnight. I have tried it twice - once when she was 6 weeks and once at 5 months - and I get so nervous that I get the runs and cannot sleep at all. I worry that I will be too tired to look after her all night and all day. How can I just relax and be myself with her and not worry so much when I take her all night? I love looking after her during the day or even in the evening while her parents are out (I KNOW they are coming home eventually so I'm okay). ANY suggestions would be so helpful as my daughter-in-law has again asked me to take her overnight or for the whole weekend and I'm in panic mode!!! Lori