I'm no electrician but i believe the min depth is now 600mm for mains type cable. You could probably get away with less for a backyard where theres not much activity on the surface.
You need to use heavy duty electrical conduit (Orange) like this:
http://www.bunnings.com.au/deta-25mm...nduit_p4330851
Place a yellow plastic sheet or even tiles on top of the conduit as a warning in case someone tries to dig it up by accident. Updating the house plans is also a good idea.
For a 10m/10a run, i would expect a 4mm electrical cable to be used but thats really up to an electrician to recommend.
Buy the parts and do the labour but get a certified electrician to hook it all up and check its all safe.
If you also plan to run data in the future, that needs to be on a separate conduit.