Good plan. We sailed a Ross 930 from RMYC to Betts Bay Gladesville in Feb 2016 in 20-25kt southerly with 4ft swell and did it heads to heads in 4 1/2 hrs. 1 reef in main and no3 jib. Dropped off some waves with no backs and got some gusts to 29kts but it went well. Left at 10am, 3 on board. Am sure you have everything covered - including logging on with Marine Rescue when 1/2 way down Pittwater and log off when at the Five Dock mooring.
www.marinerescuensw.com.au/boating-safety/log-on-and-log-off-for-safer-boating/Monday and Tuesday next week look like perfect winds.
www.timeanddate.com/weather/australia/sydney/extTrust you will have at least 2 on board? Suggest use auto inflate life jacket within inspection date and tether strap. Keep well clear of Long Reef (rock shelf goes out a long way) and North Head (wind gets affected by the high cliffs).
If you want to come down before your mooring is laid Roger at Abbotsford Point Boat Shed has hire moorings.
The yacht is comprehensively insured? You mention prior motoring around - have you sailed around also to check halyards and sheets are ok, main and jibs fully hoist ok? Battens secure in mainsail? Mainsail reef lines run? Check lifelines are ok - if one or both ends are nylon lacing lashings then ensure they are solid. Check tiller to rudder head bolts / nuts are tight - we had to tighten ours up 1/2 way down. Check gooseneck and main tack securing, clew securing. Check jib tack securing. Make sure anchor and chain are well lashed and secure and won't bounce around - ideally get them out of the bow locker and downstairs well secured but this might not be needed.