As a permanent resident you can certainly petition for your daughter, but it will take a number of years before she is able to join you in the United States. It will be helpful to look at the facts of your case to determine if there are other, more expeditious options. For example, how you became a permanent resident may provide other, quicker options.
Consult with an experienced immigration attorney who can review your case, advise you of the options available and their anticipated costs, and recommend how best to proceed.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.
Yes you can bring her here. You must file an I-130 and then wait for it to be approved and then for the priority date to become current. This process could take a couple years. If you become a US citizen in the meantime the application converts to an immediate relative petition and shortens the time to file for her permanent residency.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.