(I was helped on this post by Gorjan Alagic, Andrew Childs, Tom Goldstein, Daniel Gottsman, Clyde Kruskal, Jon Katz. I emailed them for their thoughts on the issue and some of those thoughts are embedded in the post. )
The First First Lady to have a college degree was Lucy Hayes (Rutherford B Hayes was Prez 1876-1880). Nickname: Lemonade Lucy since she did not serve alcohol.
Trivia: who was the last first lady to not have a college degree? I'll answer that one at the end of this post.
The First First Lady to keep her day job was Abigail Fillmore who was a teacher. (Millard Fillmore was Prez in 1850-1852. He became prez after Zachary Taylor died in office) .
In recent times it is uncommon for a first lady to have a day job. So much so that it was notable when Elizabeth Dole said that if her husband (Bob Dole) won in 1996 she would keep her job at the Red Cross.
For other first lady firsts see here.
Jill Biden is the First First Lady to have a PhD. (ADDED LATER- one of the comments pointed out that she has an Ed. D, Doctor of Education.) She says she will keep her day job as a professor. Four other First ladies had advanced degrees: Pat Nixon (MS in Education), Laura Bush (MS in Library Science), Hillary Clinton (Law degree), Michelle Obama (Law degree). If I missed any, let me know.
The WSJ had an op-ed that said Jill Biden should not call herself `Dr'. Inspired by that, here are thoughts on the use of the word `Dr'
1) At the 1986 Structures Conference (now Complexity Conference ) Lane Hemachandra (now Lane Hemaspaandra) gave a talk. He had just gotten his PhD a few weeks ago, so he was introduced as `DOCTOR Lane Hemchandra' Gee, most of the talks were by people with PhD's but were not introduced as such.
2) Most people I know within academia do not call themselves Dr since it sounds pretentious. However, speaking in public about an issue one might want to use `Dr' to signal that you...know stuff. However, it would be odd for a PhD in (say) linguistics to claim he knows a lot about (say) politics. It has been said: an Intellectual is someone who is an expert in one field and pontificates in another field.
3) Does the general public think of DOCTOR as Medical Doctor? Probably yes. There are some exceptions: Dr. Martin Luther King and Dr. Henry Kissinger. Also, I think it is more common in Psychology, pharmacy, education, and counseling to call yourself `Doctor'
4) The article also criticized her PhD (in education, about community colleges) as `useless' . If that's the reason to not call her doctor than I shudder to think what the WSJ would think of degrees in, say, set theory with an emphasis on Large Cardinals. GEE, you can't call yourself DOCTOR since your degree is on Ramsey Cardinals. OH, now they found an application, so now you CAN call yourself DOCTOR. OH, the application is to extending the Canonical Ramsey Theory from Polish spaces to meta- compact cardinals, so we can't call you DOCTOR after all. Do we really want to go down this path?
5) I ask all of the following non-rhetorically: Did the author read her PhD thesis? Is he qualified to judge it? Did he (as one should do) look at her entire body of work to judge her? What point is he trying to make anyway?
6) Should Dr. Who call themselves a doctor? Are they a medical doctor? PhD? If so, in what? Is `Who' part of their name? For other TV and movie tropes about the use of the word doctor, see here.
7) I avoid saying I am a doctor since people will then ask me about the medical condition.
I avoid saying I am a computer scientist since people will then ask me how to help them with their Facebook privacy settings.
I avoid saying I am a mathematician since people will ask me to help their daughter with her trigonometry.
8) The answer to my trivia question: The last first lady to not have a college degree: Melania Trump. She went to college for a year and then left. The one before her was Barbara Bush who also went for a year and then left.
ADDED LATER: Many supervillians who don't have a PhD or an MD call themselves `Doctor', see here. Why no outrage about this? Because (1) they are fictional, and (2) imagine the scenario: Not only does Dr. Doom want to take over the world, he also doesn't even have a PhD or an MD!
ADDED LATER: Where does Dr. Pepper fit into this?