I am a DL Platinum flying business class to Australia on V Australia.

I bought separate coach tickets on Virgin Australia on the domestic leg (different day).

DL's website makes it look like I can access the Virgin lounge for the domestic leg but Virgin's website is less clear. What the DL website may mean is access when connecting with an international itinerary on DL or V Aus.

Do you think they will let me (and my wife) in the lounge in SYD before our domestic flight? I would like to get to the airport early so I don't have any problems but don't really want to just sit around the airport. By the way, how is the domestic check-in and security for Virgin Australia (time wise)?

I can see what you mean; however, going by posted experience by Air NZ and Singapore Air elites who have used the (recently established) reciprocal rights, you will have access before a DJ/VA flight.

The domestic check in on DJ is good if you can use the premium facilities (which you should be able to as a DL Plat).

If checking bags allow 1hr to 45min, and remember baggage check in closes 30min before departure. Look for the premium check in (purple signage/carpet). If you have hand luggage only and you are checked in online, then you just need to be at the gate 15-20mins before departure, though if you are in the Virgin Australia lounge, you can generally wait till they call the flight.

At Sydney T2 (Virgin Australia's domestic terminal), you can use the premium lounge kerbside entry (often no wait for security) if you have hand baggage only; if you have baggage to check you need to do this at the main check-in desks, but it is often quicker to then walk outside to the drop off zone and to the kerbside entry to the lounge (turn left and it is just past the the last entrance to the main check in hall) than to go through standard security. At any airport other than Sydney there is usually priority security which helps speed things up.

and if you were not aware, Australian domestic security is nothing like the US.

There is no liquid or gel rules (take whatever you like), no shoes off, only WTMD, random ETD, but laptop must come out for x-ray. Oh, and no ID check, shouting or rude attitude from the screening staff either.