If you're building your own DET10 (a great biased photodiode!) they use the FDS010 inside.
(Smaller active area, faster rise time) but for the Q-switch frequencies you'll be measuring... either should be fine.
Why the 980nm laser diode?
If you're just using it to test the photodiode circuit... <5mW red diodes would do; hookup the modulation line of the diode driver to a signal gen, and monitor commanded + observed signal. The diode driver will be the "slowest" link in the chain.
I know you said it was problematic in transport... but should you ever be able to bring your YAG to the office, you can use all those tools to measure yours [DET10 / Coherent Labmax-TOP / Spectrometers etc.)
(or bring yourself + have a go with one of the units there)
What do you want to achieve? Just learning? Or a specific task for the bigger laser?
Photodiodes saturate with a few µW's-mW's; so either position it "near" a high powered beam, or use ND filters (not advisable for your Q-switched laser!)
Dan