Hello!
Anywhere with good bus and/rail links I suggest in the absence of a car. Canning Bridge train station has good connections by bus to Curtin and by rail to Leederville so anywhere around there could work eg Como, Manning (higher crime in parts) or if the budget allows, Applecross.
I've heard good things about South Perth Primary. Unsure about Como in terms of government schools as our kids are in the private sector - at the moment. We may move the youngest to Como Secondary given the EMiTS program (a quick google search will give more info). For South Perth Primary you'll need to be zoned to the school to guarantee attendance there. Their website should provide zoning or 'catchment' information. If you go private eg Wesley College in South Perth, so long as you can pay the bill you're in..or should I say bills (endowment fee etc.). That said, there is or certainly used to be quite the waiting list for Wesley.
Personally, I'd be looking ahead to what secondary schools are around and good particularly in the state system (assuming that's your preference). I wish in hindsight we had done that. Check out Rossmoyne, Applecross (although recent reports aren't so good) and Willeton. There is also Perth Modern for the super smart kids by way of an entrance exam - well worth the move but do your research and know the cut off dates).