Can my husband and I still claim my 23 year old college student on our taxes if she got her own medical insurance in November 2019?

Yes. Her medical insurance has nothing to do with her dependency.

Qualifying Child

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.

note the "principle residence" definition - living away in an off campus apartment while in college doesn't change your child's "principle residence' from YOUR home.  The IRS considers that off campus apartment (or the dorm) as 'temporary residence' and the permanent residence is still YOUR home.