Yes and yes. It sounds like she did a great job getting through high school early but was still enrolled for those 5 months and qualifies as your dependent under age 19 on December 31. The IRS has a quick quiz for your peace of mind. See Dependent 

Q. Would she still qualify as a full time student?

A. Only if her high school classified her as a Full time student. See below.  If the school does not distinguish between full and part time students, and can't give you an answer; I think you're safe in claiming her since she is enrolled, as a student.  But, I cannot find any reference for that opinion. 

Q.  Also would her being 19 as of January 2024 disqualify her as a dependent even though she would likely considered to be a full time high school student? 

A. No. But it  would disqualify her if she is not considered to be a full time student. 

Q. When filling out my taxes on TurboTax it says she qualifies. 

A. That's because you are answering yes to the questions is she a full time student.  Which she may  or may not actually be. 

From IRS Publication 501 (Dependents)

"Student defined.

To qualify as a student, your
child must be, during some part of each of any 5
calendar months of the year:
1. A full-time student at a school that has a
regular teaching staff and course of study,
and a regularly enrolled student body at
the school; or
2. A student taking a full-time, on-farm training course given by a school described in
(1), or by a state, county, or local government agency.
The 5 calendar months don't have to be consecutive.
Full-time student. A full-time student is a
student who is enrolled for the number of hours
or courses the school considers to be full-time
attendance.
School defined. A school can be an elementary school, a junior or senior high school, a
college, a university, or a technical, trade, or
mechanical school. However, an on-the-job
training course, correspondence school, or
school offering courses only through the Internet doesn't count as a school."