We just moved to Earlsfield and it is very baby friendly!
We found a place with some grass in the backyard (houses in Northcote area seemed to have very small "gardens" it is also cheaper in Earlsfield) and we can walk to Wandsworth common. Earlsfield station is great with trains running every 4 or 5 minutes - 3 stations to Waterloo (though trains are busy)!
Here are some links to some previous posts listing a few playgroups and events / activities in the area:
http://www.nappyvalleynet.com/events-in ... t8651.html
http://www.nappyvalleynet.com/playgroup ... t2229.html
http://www.nappyvalleynet.com/playgroup ... t8641.html
The 'events in Earlsfields' posts seems to be updated regularly - which is really great.
Don't think you could find an area that is more baby/toddler area than Earlsfield/Southfields. Seems most of the general area is full of babies - if youwalk around it seems to be just buggies everywhere!
As for nurseries there is suppose to be a new one opening at the top of Magdalene Road. We have a baby in Mayfield Children's Centre and so far really love it (someone just posted about it on here somewhere and I agree with the posters comments). I think you can find some info on other nursery options on here if you do a seach. Sticky Fingers is another one I was interested in.
Good luck with finding a place! We really love the area!