As per US Immigration rule... she will loose US citizenship if she take anyother citizenship.. US only allow you to be dual citizen ONLY if you get US citizenship by naturalization and your country (where your born) allow you to have dual citizenship.
This answer is wrong. As Seym wrote, both the U.S. and Canada allow dual citizenship, so your child can get Canadian citizenship while keeping her U.S. citizenship. The only way for your child to lose U.S. citizenship is by renouncing it, but she would have to be at least 16, and most likely 18, to do so. See:
https://hodgen.com/its-hard-for-minors-to-expatriate/
There is definitely a benefit to keeping U.S. citizenship, in that your child would have the option one day of working and/or living in the USA without restriction. The downside, however, is that once your child starts earning a certain amount of money, she will have to file a U.S. income tax return each year, even if living in Canada. (There is a tax treaty to prevent double taxation in most cases.) In addition, there are numerous U.S. tax rules that will affect your child's everyday financial life, such as having a savings or chequing account, investing money, etc.
Is the freedom to live/work in the USA worth the financial hassle? Your child will have to decide that for herself as an adult. However, there's no reason for her not to become a Canadian citizen, because the problems are all on the U.S. side, and the child is already a U.S. citizen.
*Technically, a person can lose U.S. citizenship by taking a foreign citizenship IF the person intends, by taking a foreign citizenship, to give up U.S. citizenship. However, the U.S. government no longer recognizes such a loss, and all persons are required to visit a U.S. embassy or consulate and pay a fee (currently $2,350) to formally renounce if they want to give up U.S. citizenship.