hi there! welcome to the area! it depends what you want-there's a lot for a little one.
there's a lot of mother and toddler groups (but most in term time though).
we have taken DD to Kent Life near Bearsted for years - you can get tickets to last a year and then visit as many times as you like-there's a nice outside play area and soft play inside and there are tame animals for your little one to meet. tea/coffee for you isnt extortionate either.
same for leeds castle-but maybe not so much there for her while this young? there's animals there though and a play area and ticket lasts a year.
there's kidzone but i would go when kids are at school when only younger kids are there and not pushing when they run about!
we took DD to the Rochester esplanade a lot to the swings there as you can walk along and look at the boats
give me a little while and i'll think of some more but got to put dinner on.....