The Lizard is a coastal area in cornwall. That's all I know ( except we went to a festival there years ago and it was back of back of back beyond ) Both it and Lands End are further west than perranporth. Bear in mind there are no motorways in cornwall, dual carriageways are a big as it gets, so journeys can take a little longer than you might think as you are more likely to be driving at 50mph than 70mph.
Find the nearest tourist office (there's one in Perranporth) & get yourself a copy of the Visit Cornwall (or whatever it's called this year) booklet + handfuls of other flyers, and just pore over them (wine in hand) the first evening.
Cornwall is bursting with things to do, & they're generally very well publicised. The issue is picking the things that are exactly right for your family - so, eg, your 10 mth old won't want to spend a day in an amazing elaborate maze made of maize plants (though my 9yo will) but she will want to look at the bunnies at Dairyland (whereas mine won't).
It used to be quite nice in a remote barren John o' Groats cliff top sort of way, but it's been turned into the worst kind of rip-off amusement park.
If you look at the shape of Cornwall, the Lizard is that chunk looking like a heel, to the east of Land's End. There is a fantastic homemade organic ice-cream farm deep down in it - long pilgrimage from Perranporth though.
(NB everywhere in Cornwall is much further from everywhere else than you'd think - small roads, tons of holiday traffic - don't drive about unless you really want to.)
Don't go to Land's End. Or, rather, if you want to go there, don't pay to go in, but drive to Sennen Cove and walk to Land's End on the coastal footpath (dog will love it). The beach at Sennen Cove is one of the best in Cornwall.
The Lizard doesn't have 'attractions' as such, but is itself stunningly attractive (IYKWIM). On the Lizard peninsula, Coverack is lovely and Kynance Cove (NT, so you pay to park) is stunning. The Lizard village (which is about a dozen houses IIRC) has one of the best pasty shops in Cornwall.
Be careful with your dog anywhere where there are dunes and marram grass (e.g. Hayle Towans). The marram grass is a great breeding-ground for adders, and my parents tell me that this year has been particularly bad for them.
TBH with a 10-month old, I'd avoid attractions aimed at children and just do what you and dh want to do. You'll have plenty of time for farm parks and playgrounds in future years.
There is a little book called Kids Cornwall that is available in tourist centres down there that is brilliant. Costs about £3 and published as a fundraiser for a local school. It's got loads of ideas for wet days, kid friendly cafes etc - worth getting if you see it.
Beautiful places to go are also the Roseland peninsula and the Helford Estuary. Falmouth is nice and the maritime museum there is interesting (also good with older children).
A good dog-walking place near-ish to Perranporth is Tehidy Woods. Another favourite dog walk for me is up the river from St Erth to Rosudgeon (you'd need baby in a sling/back-pack for that one, though, as there are stiles). If you don't mind a bit of a climb and you want amazing views, climb Trencrom Hill (again, doubt you'd get up with a buggy, though). From the top you can see north and south coasts simultaneously (from Mount's Bay round to St Ives Bay). You probably already realise that dogs are not allowed on most beaches in the summer months. They are, however, allowed at the north end of Hayle beach.
St Michael's Mount is worth a visit, too.
<<Ellbell wonders if she should be working for the W. Cornwall tourist board >>
St Michael's Mount is a semi-island, joined to the mainland (at Marazion) at low tide by a causeway and accessible by boat at other times. The building at the top was originally a Benedictine Abbey (like the one at Mont St Michel in Normandy) but is now a stately home, partly open to the public (though still lived in in parts) and managed by the National Trust.
Hey Foxy go to St Ives. You've got The Tate, Barbara Hepworth's studio and gardens, lots of lovely cobbled streets to get lost in. Get the train there - lovely views. The Eden project is worth a go and I def. second Sennen Cove - its beautiful. We stayed at a weird B & B a walk away from Sennen and lands end. We walked to lands end but didn't bother with the tourist fandango as it looked pants. Are you getting excited?
B & B was weird because we couldn't work out if the owner was a man or a woman. Plus we had a ensuite actually in our room - i.e shower . Toilet was in a cupboard! I kid ye not. Was hysterical having a shower infront of DH lying in bed! It was manky leaky thing but we can honestly say we're so glad we stayed there.
Very jealous as I love St Ives. Great friend who died a few years ago lived down there and if only he'd decided to stay there may still be around.He was such an amazing painter and every time I visit it I always remember the times I spent with him. Great fish restuarants and beaches....ahhhhh.