Ohhhhhhhhhhhhhhh so much to do. We love holidays in Dorset.
Corfe Castle itself is national trust and worth a half-day amble around with the toddler. The steam train runs from corfe to Swanage, where you can play on the beach etc.
Brownsea Island is national trust as well (although you have to pay for the boat trip too) and if you are members Kingston Lacy is a gorgeous house and gardens that is also NT. The ferry goes from Poole Quay, which in itself is interesting for a potter and there is a lovely park - Poole Park, just around the corner. Great for feeding ducks, climbing trees (there are some fallen on the ground from a storm), Play areas, large lake with pedalos on etc. You can walk through from Poole Park to Baiter/ Whitecliff which has gorgeous views of the harbour and the Islands, and a good path alongside the water.
Durlston Country Park (nr Swanage) is a lovely place to walk, although there is a bit that is next to the cliff edge without a wall. There is a lighthouse, a huge globe and a visitors centre too there as well as lovely walks.
Farmer Palmers is nearby. It is an expensive day out but it is such a lovely one for toddlers. You can spend the whole day feeding animals, going on tractors, etc. and ideal for a toddler.
However, I suspect your child will just enjoy going along with whatever you fancy at that age, and just enjoy being out somewhere new with you. There are some amazing walks in the Purbecks. (One we like is to park in Kingston, along the road from the Scott Arms pub which has a gorgeous view of Corfe Castle and walk to Swyre head ( www.jurassicjaunts.co.uk/Kingston_to_Swyre_Head.aspx ) Not sure I'd want to take a pushchair but our child managed it at 2 years old and we had a picnic at the end. One of my favourite Dorset views up there!
Let me know what sort of things you enjoy and I'll have a think.
Depending on what direction you're coming from Moors Valley country park has a great "play trail" with lots of outdoor play equipment along the walk.
Studland is a lovely beach, less touristy than Swanage/ Poole/ Bournemouth (free parking if NT). You could go from there across on the chain ferry to Poole which is fun. (Lovely hotel the other side - the Haven, if you fancied a coffee).
Arne is a nature reserve with a couple of walks that have views of the harbour, if your toddler likes woods.
You could take a boat from Poole quay up the Wareham river...