My daughters mother and I live together, we are not married, she claimed our daughter on this years taxes, can I claim our daughter too?

You can't both claim the same child in the same year. You can decide between you which one of you will claim your daughter each year. If you can't agree and both of you claim your daughter, the IRS will let whichever one of you has the higher Adjusted Gross Income (AGI) claim her.

No, your daughter can only be claimed by one parent, not both.