Interestingly, if we look at the 'Doctor' career in CT's Citizens of the Imperium (Supp. 4), there's no advantage to enlistment, etc. from Edu. Int gets you enlistment and survival bonuses, and Dex gets you a big enlistment bonus at Dex 9+ (so not just good enough to be a surgeon, but enough to be a notably dexterous surgeon). Doctors gets Merical-1 upon enlistment. Past that they've a 2-in-6 chance per roll on the service skills and both education tables, and can get +1 Soc on the personal development table. The better education table gives them chances of +1 Int or +1 Edu rather than repair skills, while the service skills table might get them +1 Dex (or skill with a melee weapon - it's clearly the 'street doc/'chop shop surgeon' table).
Given doctors have no commissions or promotions, and do not get extra skill rolls past term 1, most full doctors will not be particularly young (average of five terms to get Medical-3). However, COTI pre-dates the '81 version of the LBB, so I'd allow them (and the other no-position careers in COTI) two points per term, like Scouts got, making the average number of terms to qualify 'only' three.
For what it's worth, in MT the Advanced Education tables, due to some of the cascade skills having Medical in them, has a higher chance of getting Medical, and doctors average only needing two terms to qualify.
In both editions Doctor is one of the wealthier careers.