Can anyone suggest a caravan park within about an hour by public transport from the city

How,

Welcome to the gang Bill and Sue, enjoy here and out in the playground.

Pakenham CVP is not that far. There is also one in Frankston Dandenong Rd Dandenong South.

If you want to be north - off the Hume Freeway, Highlander Caravan Park in Seymour is a great spot - reasonably priced, and the train goes into the city, country train, so lots of comfort. Friendly owners, clean amenities, and walking distance to shops, club, and railway station.

Depending on where you wish to be situated, the Berwick showgrounds are fantastic. Power and water, close to everything and transport into the city.