Congratulations on your baby! I did FLM a couple of years ago when my son was 8 months, so probably a similar timescale to you - ran/ walked for about 4 weeks from a month after the birth, then gradually built up frequency / duration of runs so I was ready to start a 14 week training programme around Christmas.
The best advice I can give you is to post on this this thread - Mums' running club . Lots of lovely ladies who are all running with young children and have loads of experience and advice to share.
Carovet - only skimmed through but I saw you were having problems with MEOS - I use shaped fleece liners I made myself which pretty much cover the inside of the nappy - sort of an hourglass shape but bigger at the back than in front. I could send you one to use as a pattern if you wanted to make some (I just used standard fleece material from John Lewis).