Yes, she'll be fine. You need to do some things for yourself/your career and this is a wonderful case of having a totally trusted person who can care for your child without your worrying. Go for it.
It sounds like your girl would not be in your own home but in grandmother's house. If possible, I'd have grandmother come take care of her in your own home where things are most familiar to your little girl. Unless your daughter has already spent plenty of multi-night trips away to grandma's I would opt for her staying in her own home and own bed, so there is less change overall.
You don't say how far off these trips are, but if they're not coming up soon, you could do some "dry runs" of overnights with your mom handling everything while you're still in the house but staying as hands-off as possible, or even with you going away just over one night (visit an old friend!). Might increase your mom's confidence level and get your daughter used to the idea. Ignore this suggestion if your mom already spends a lot of time caring for your daughter!