I went to Phi Phi just before Christmas. The ferry trip from Koh Lanta to Phi Phi was good and although I didn't have a child with me, I would guess is buggy friendly, as is the ferry to other way to Phuket.
Phi Phi - if you are staying in TonSai (town) then you would be fine with a buggy as that is where the ferry stops, so there are a few roads etc. If you are staying elsewhere, then bear in mind there is no road transport on Phi Phi - everything is done via long tailed boats, which may prove challenging with a baby and a buggy - we had to wade out to the boat, then climb some rickety steps to get in it. Once in it you need to climb over the benches to get to the seats (no aisleway). I didn't stay in TonSai, but would suggest with a buggy it is easier than other places on the island.
We stayed at the Holiday Inn Phi Phi at Leamtong Beach, which was about 25 minutes or so on the long tail boat from TonSai. Once there, you get taken on a sea tractor from the boat to the hotel. The trip back involved climbing off the long tail boat into the ferry out to sea (to do with the tides I think) so definitely not for the less mobile. A few restaurants along the beach, but mostly high star hotel complexes. Several vendors on the beach with boat trips, one of which is to 'The Beach' where the Leonardo de Caprio movie was shot.
Short of island hopping every day, I am not sure what you could do with a small child - snorkelling, diving etc would be out, although the beach at Leamtong is very nice and is shallow when the tide is out. Holiday Inn had 2 or 3 pools.
Koh Lanta was a nice island, perhaps a bit more going on than Phi Phi. We stayed near Saladan which had plenty of bars and restaurants - really nice authentic Thai village really. Stayed at the Chada Lanta hotel which was right on the beach. Several trips around Koh Lanta via boat and tuktuk available - might be easier with a buggy?
Kata Beach resort, on the Phuket mainland was also nice - huge beach, smaller beach cove next door, plenty of really nice eateries etc. Lots of boat trips, tuk tuks, taxis. We had a speed boat day trip to Phang Ngar (James Bond Island) which was a nice day out, including an elephant sanctuary and a trip round a floating village.
If I can help with any questions just ask!