I do empathise that being a working parent with a young child wears you down. I returned to work early with my son and will do the same with this baby, as my partner was studying full time with my son and is now in a graduate job that pays rubbish for another couple of years, and I earn more. I find the grind of the daycare routine, the guilt and always being busy has often left me a bit drained and resentful.
But I think the big problem is housing costs. the average mortgage requires either one very high wage (why didn't I marry a medical specialist, lol) or two average wages. The carbon tax pales in comparison with killer housing expenses.
eta: are people getting that much from the government for carbon tax? We only earn about $85k combined at the moment as we both work part time, and we got $36.50 as a lump sum payment as we receive a little family tax benefit each year (one child). But we will both get tax cuts as we both earn under $80k.