If you deposit the money in your account, it will count against the gift tax exclusion for you, not your daughter.
As such, you should open a bank account for your daughter. Assuming she already has a social security number, this will not be complicated. Otherwise, apply for one, as mhoran notes before the end of the year.
The kind of account you should open depends on the purpose of the money, but likely it should be opened as a Uniform Gift to Minors Act, or Uniform Transfer to Minors Act, account. This means it is your daughter's account (not yours), but you designate one or more custodians who are the ones who can actually make withdrawals. Any money in this account must be spent in your daughter's interest, but it's not required to be spent with her approval (even as an older child) nor on a specific thing (it's not just college money, like a 529 account is).
Before you do so, you should consider how to set up custodianship. Some parents simply make themselves custodians; some ask another relative to be custodian or joint custodian, or even someone like a godparent or close trusted friend. Having a joint custodian is helpful if you feel like it may be challenging to not dip into the account if you had financial difficulties (as both custodians must sign off on withdrawals).
Finally, you should consider whether you want this to be a simple bank account, or whether you might want to consider something like Vanguard or Fidelity investment account. If it's likely to contain over $10,000 or whatever the reduced/no fee limit is at the investment firm you choose, it may well be worth your while to do this as you can earn significant returns fairly safely, assuming the money is intended for longer term use (for college or other later-in-life uses).
Note that for tax purposes, this gift will count for 2016 taxes regardless of when you actually set up the account, as you have "constructively received" the gift when the check was given to you. So there's no rush to work this out before the end of the year; you can still deposit it next year. However, your daughter needs a SSN to be able to be claimed as a dependent on your taxes, so that at least needs doing before the end of the year.