Q: Is it normal to need the brake pads and rotors replaced at 34K? on 2005 Mini Cooper S

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The invoice stated the brake pads were 5 mm.
(3) Answers
You need to know the original thickness of the pad to know what 5mm represents, if the pad is 10mm when new, then you have 50% remaining. Pads should be replaced at about 20%.
The rotors have a minimum thickness as well, and if they are recommending rotors, they should state the measured thickness of the rotor. If you have vibration from the brakes, then you may need rotors no matter the thickness measured.
It sounds like they are over selling this job and you don't quite need brakes yet, I would get a second opinion, and/or ask for a better justification as to why the pads and rotors need replacement.
This was suggested to me as well. I purchased the extended warranty and the dealer was very happy to replace it...of course. My car was at 55k miles.