My dependent that I was trying to claim did not start work until the middle of October ..why cant I claim her for all the other months?

Did she make more than $4,050? If she made more than this and doesn't qualify as a qualifying child you would not be able to claim her.  How old is she and was she a full time student?

It doesn't work that way. You have to look at the year as a whole. She would have to meet one of two tests to be your dependent. If she is not a qualifying child, then look to the qualifying relative test.

In general, to be a taxpayer’s qualifying child, a person must satisfy four tests:

Relationship — the taxpayer’s child or stepchild (whether by blood or adoption), foster child, sibling or step-sibling, or a descendant of one of these.

Residence — has the same principal residence as the taxpayer for more than half the tax year. Exceptions apply, in certain cases, for children of divorced or separated parents, kidnapped children, temporary absences, and for children who were born or died during the year.

Age — must be under the age of 19 at the end of the tax year, or under the age of 24 if a full-time student for at least five months of the year, or be permanently and totally disabled at any time during the year.

Support — did not provide more than one-half of his/her own support for the year.

Qualifying Relative

• Do they live with you? Your relative must live at your residence all year or be on the list of “relatives who do not live with you” in Publication 501. About 30 types of relatives are on this list.
• Do they make less than $4,050? Your relative cannot have a gross income of more than $4,050 and be claimed by you as a dependent. 
• Do you financially support them? You must provide more than half of your relative’s total support each year.