As a parent of a child who takes lessons in both violin and piano -- your daughter might find piano hard too, once she's past the early lessons. Piano at first is an instrument where it's attractively (and deceptively) easy for anyone to make some form of music -- one finger plunking on keys can sound sensibly like music, whereas on a violin, it's much, much harder at first to get a musical sound; there can be a lot of scratching and screeching at the start that discourages kids. That's why your child might have started too young (for her) on violin; she's not ready to work enough to get past that initial barrier.
Have you asked her why she wants to quit it? For instance, if she's not practicing, have you asked her why? Maybe she will admit "It's too screechy" or "I can't get it sound like music or hear the tune" or even --and eight weeks in this is typical -- "I've got a blister on my finger and I hate that." Ask her. Do you feel she's with the right teacher? She might be fine with going to her lessons, but is the teacher experienced with kids this young, and does the teacher give her specific things to practice each week? Does she "click" with the teacher and want to please this person? That helps a lot with younger kids--wanting to get the teacher's approval.
I might talk to her violin teacher. I would bet that the teacher sees this all the time -- kids who drop out after a few months. Ask the teacher what the teacher and you can do to motivate her; for younger students, some teachers offer little rewards for completing certain pieces or for practicing so many minutes in a week, for instance. Or the teacher might have insight such as "Most kids feel frustrated at 8 to 10 weeks but if they stick with it and practice even a little they tend to get music out of the instrument by around the fourth month" and so on. These are the kinds of experienced insights our daughter's violin teacher always has and they do help.
Based on what the teacher says, I might cut a deal with your child where she continues for another two or three months-but with a plan and rewards for practicing. It can be minimal but needs to be consistent. Yes, it is fine to provide incentives -- bribes if you will -- for a kid this young, and to set up practice charts that result in, say, ice cream at the weekend for X minutes of practice in the week. When she's older you won't need to do this with instruments or anything else.
I'd talk to the teacher (without your child present) to talk about some incentives and a plan for practice times with a specific time and place for practices. If a kid is just told, go practice, it might have the same effect as "Go clean your room" -- it's overwhelming, it doesn't give specifics, and many kids this age need a little more direction or they'll give up. That's why if the teacher cheerily says, "Spend 10 minutes a day on these 10 measures of this ONE piece," and you support that with a good music stand and a time each day set for practice, plus incentives, it could help. A practice chart is good (they sell them at music stores but you can make your own; it might go better if the teacher gives her one, so it's something she's doing to please the teacher, and doesn't feel like a chore assigned by mom).
But if you just don't want to go there with another few months and more emphasis on practice, then do have her stop. But I would not let her jump to piano. If she's not ready to practice violin, she won't practice piano either once the initial fun has worn off and she has to use more than one hand, and there is no point doing lessons without at least some minimal habit of practice that she's willing to do. The catch is, if you wait too late, she won't want to try at all. But I'd tell her that if she wasn't willing to practice violin, she can't just switch to piano lessons as it's not fair to teachers to take a slot in their time and then quit on them, and you and she can revisit instruments in a few months. Meanwhile, expose her to a lot of recordings of good string and piano music and take her to concerts if you can --doesn't have to be expensive professional stuff, take her to the middle or high school orchestra concerts which are free!
Does your elementary school offer a strings program? If you decide to just stop for now, consider having her do strings when she's old enough. In our school system kids can start strings in fourth grade but not earlier. By fourth grade, the kids are more ready to try, and even better, they are doing it in a group setting and performing as a group. Does your school system offer violin (orchestra) as a class in elementary school? If so, I'd find out when it starts, probably fourth to fifth grade, and wait until then but try again. Playing in a group can be very motivating for kids, and if the school has a good strings teacher, your child will be required to practice a certain number of minutes a week as part of her grade (also a big motivator).
My daughter (now 14) started violin in school orchestra in 4th grade and piano lessons at home at the same time (yeah, crazy, I know, to start two at once). So she's pretty aware of the different demands of the two instruments, and she has said that she prefers violin because piano requires a lot more note-reading!