I would definitely recommend having someone there specifically for your daughter--if you don't have a friend or family member you're comfortable with, then hire someone.
1. For your daughter's needs: She might need a snack or help in the bathroom and you might be in transition. There should be someone there to help her, and it shouldn't (have to) be your or your partner. Or she might become frightened when she hears you making a lot of noise, or sees what looks like a lot of blood. She should have the option of leaving (at least the room) if the situation becomes stressful for her, and she shouldn't have to go be alone in that case. Also, she might not know that she needs to leave if she becomes scared--she may need a caring adult to notice that she is scared and suggest that they go play upstairs for a little bit, or whatever.
2. For yourself: It's hard work having a baby, and it's hard work tending to your child's needs. You shouldn't be expected to do both at once, and since you can't delegate the former, you should have someone to entirely relieve you of any responsibility surrounding your older child. As an apprentice midwife, I've seen several situations where a woman has mild or inconsistent contractions all day, that just aren't "going anywhere," and then she puts the kids to bed (or they go to Grandma's, or whatever) and her labor picks right up, progresses and she has a baby. It is mentally and emotionally taxing to worry about your child, as your will naturally do if she becomes scared, or ill, or upset because no one is getting her a glass of water, or *whatever.* Let yourself entirely off the hook by finding someone you can entrust her with, and then focus on having your baby.
3. It is possible that you will need to transfer to a hospital, perhaps emergently, perhaps not. Let's say you transfer for pain relief--it's not a good time for your partner to have to worry about getting your daughter's shoes on, and getting her in her carseat, and whatever-else needs to happen with her, while also trying to support you in what has become an overwhelming situation (enough to warrant the transfer) and prepare things like the baby's car seat and your hospital bag. Your partner should be allowed to focus entirely on you at this moment--and you shouldn't have to deal with your daughter at the hospital if you don't want to. Leave it to someone else to care for her in that moment, and let your partner focus on you and the baby. And although it is unlikely, you could have a more emergent transport, for a hemorrhage or a baby who is in trouble. In that case, it may be dangerous to you or the baby to be held up by dealing with your daughter. You and your partner should be able to simple load up and leave, without having to worry about her in that moment. (I don't mean to sound alarmist here--I've worked with the same midwife for 3.5 years, with very few transports, and none of them particularly emergent--but when that need does arise, there is enough stress without having to deal with an older sibling in that moment. I was at one birth where a mother had to be transported by ambulance postpartum, and her husband, who would have really liked to have ridden in the ambulance with his wife, had to wait at home until he could get a hold of someone to come be with their older child, and then wait for her to drive to their home. In the end, everyone was fine--but it was really stressful for him to be separated from his wife at that time, and I imagine it made the situation extra stressful for her, as well.)
Good luck! I think having your other child(ren) at a birth can be a really wonderful experience for everyone--and by being fully prepared, you significantly increase the likelihood that it will be so!