Cantilevered Verandah Roof

Greetings all, this is a first post having observed lots of useful information for some time.

We are in Perth in a 60 year old jarrah framed house in good condition. We want to add a cantilevered varandah roof over our back laundry door, can't do a vertical supporting post because of vehicle access. Dimensions are 1.9m x 1.9m. pitch of 20% carrying zincalume roofing. Back door is in an alcove, so a beam out of each wall, and then fixed back into the wall diagonally at the internal corner of the alcove (using the ridge as strucural). (If I work out how to add a drawing I will!) I figure construction of treated pine will be lightest, but unsure of the dimensions and material to use for the beams which will be anchored back into the existing framing. There is almost no limit of what lenghth can be fixed into the wall framing, but I presume the important part is really the stress @ the pivot point where it comes out of the wall.

I am an adept woodworker and house renovator, not much terrifies me when it come to playing with timber houses.

Any ideas, or job for an engineer.

Thanks hopefully.

PS: Not averse to working in steel either if necessary.