It's not that big so technically everywhere is in walking distance of the village centre, however some bits are more hilly than others :) The estates up by the High School at at the top of a steepish hill. At the other end you have the area around Newton Primary which, looking ahead, is a long walk from the High School and no transport for the kids is available.
The council estate is George Street, edward street etc. I don't live in Dunblane so can't comment on whether these are generally ok or not.
I'd watch on the property listings hough as it often describes places as being in Dunblane when they aren't, just click on the Map and you can see where it is. Essentially Victoria School is the extent to the North and Dunblane High to the South. The A9 which is effectively more or less Motorway runs up the West side and Farmland/Golf course etc to the East.
There is a Tesco near the Railway station, an M&S food fairly near that and village shops such as butcher etc. There are a couple of pubs/cafes. There is loads going on in the Dunblane Centre for all ages so that's probably a good starting point for you when you move in.
Remember there is no petrol station so you need to remember to fill up when you are out in Stirling. Much larger supermarkets in Stirling and more pubs and shops in Bridge of Allan which is technically walkable and you can go via the Darn Walk cross country when the kids are bigger. Refuel at the Allan Water Cafe with Fish and Chips and Ice cream.
Happy to help with any further info, but my main interaction is with High School so I have limited knowledge of what is there for toddlers :) All the primaries are well thought of so that probably shouldn't influence your decision.