Recently flew Sydney to Brisbane on a Qantas 737 with inflight Wi Fi enabled and took the opportunity to record a couple of results.
The actual aircraft was VH-XZP a Boeing 737-838 Serial number 46577-5164 painted externally in the Qantas retro roo livery.
Seat pitch on the newer Qantas 737-800 with 30 rows in economy is very tight compared the the older generation Qantas 737 with 29 rows in economy and these aircraft would be uncomfortable for flights more than 2 hours or so in economy. To check which aircraft might be servicing an intended route expert flyer is a handy tool but there is no guarantee an aircraft change can take place. For longer haul in economy the exit rows would be worth the additional $20.00
Anyway the inflight Wi Fi internet was turned on after the doors were closed and I connected and ran a speedtest while still on the ground at the gate in Sydney;
There were a few dropouts and timeouts after take off, I tested streaming internet radio but the connection was not stable enough for this type of use with dropouts occurring.
Between Sydney and Brisbane approaching the midway mark at cruise altitude I ran another speedtest,
The connection was more than adequate for sending and receiving emails as long as one is prepared for the occasional timeouts which is to be expected with satellite and higher latency with satellite.