Native speakers have a very strong preference for using perfect (or pluperfect) after nachdem. The conjunction seems to almost demand it. The reason for this formal requirement is probably semantics.
The perfect has a double function in German: on the one hand, it is a past tense, pretty much interchangeable with the preterite (simple past); on the other hand, its meaning is aspectual, signifying that a result state persists.
A simple example where preterite and perfect are not interchangeable:
- Ich trank zu viel.
- Ich habe zu viel getrunken.
The first sentence will be interpreted as a habit in the past. The second has another interpretation, as talking about feeling drunk or ill at the present moment (as a result of having drunk too much). (Note that, in accordance with what was said in the second paragraph, the second sentence can also be synonymous to the first one.)
In your example, the perfect seems to be required by the meaning alone:
Ich werde fahren, nachdem ich gefrühstückt habe.
Many speakers would use wenn or sobald instead of nachdem here and, although the former conjunctions are not limited to the perfect in general, they are in this context. The idea is that breakfast has to be over and, presumably, some state of readiness or at least satiety be reached, for driving to commence.
Ich werde fahren, sobald ich *frühstücke / ✓gefrühstückt habe.
Ich werde fahren, wenn ich *frühstücke / ✓gefrühstückt habe.
Two general remarks: 1. Germans would probably use present tense fahre instead of werde fahren in the above sentence – the present is the neutral way of talking about the future. 2. There is no consecutio temporum (sequence of tenses, e.g. backshift) in German.
There are rare cases where nachdem does seem to combine with a present.
Nachdem er sitzt, steckt er sich, mit unvergleichlicher Noblesse, eine Zigarette in den Mund. (from the DWDS corpus)
Sie sollten Ihrem Kind möglichst bald, nachdem es anfängt zu zahnen, ein gesundes Ess- und Putzverhalten angewöhnen. (colgate.de)
In both cases, most people would use the perfect instead, although it is not required by meaning; by which I mean simply that, when switching to another conjunction, the present appears unremarkable.
Als er sitzt, steckt er sich …
Sie sollten Ihrem Kind, wenn es anfängt zu zahnen …
(The example with sitzen is interesting in that sitzen is the result of sich setzen, i.e. it signifies a result state on a lexical level. Accordingly, the latter would require perfect in order to express the same idea, i.e. that the cigarette is lit after and not during the act of sitting down: Als er sich gesetzt hatte, steckte er sich …)