If I co-signed a lease for my daughter however she never signed but did move into the apartment, am I liable for rent if she moves out early?

As a co-signer of the lease, you are liable for the rent for the balance of the term of the lease or until the place is re-rented if your daughter moves out early.  When the place is re-rented, your obligation to pay rent ends.

The landlord has to mitigate (minimize) damages (the amount the landlord claims you owe) and cannot allow the rental to remain vacant for the balance of the term of the lease without making reasonable efforts to find another tenant.  If the landlord allows the rental to remain vacant for the balance of the term of the lease without making reasonable efforts to find another tenant, the landlord has failed to mitigate damages and the landlord's damages witll be reduced accordingly.  Reasonable efforts by the landlord to find another tenant are determined by what other landlords in the area are doing to attract new tenants; for example, posting a sign on the premises advertising the vacancy, advertising the vacancy in the newspaper, in a local rental guide, online, etc.

When the place is re-rented, your obligation to pay rent ends; however, if the new tenant is paying less rent than your daughter's rent, you may be liable for the difference in rent for the balance of the term of your daughter's lease.  The landlord has to have a valid reason such as market conditions for charging the new tenant less rent.  If the landlord does not have a valid reason for charging less rent to the new tenant, the landlord has failed to mitigate damages and the landlord's damages will be reduced accordingly and you may not be liable for the difference in rent for the balance of the term of your daughter's lease.