Going home outfit HELP!

When my baby is born in August (in Australia) it'll be smack bang in the middle of winter. It's already winter here now and the trips to the hospital for midwife appts are absolutely freezing so I'm a little concerned about what to dress him in to leave the hospital...

I was thinking a singlet, onesie and beanie but the singlets and onesies are very thin and I'm worried he'll be cold... I was thinking of covering him with a muslin blanket once he's secured in the capsule but not sure if that's safe and the hospital will let us leave like that. Ideas are very much appreciated! Thanks