Firstly, nice work in setting something like this up. Personally I'd edit your post and give the background information after you get into the nitty-gritty of what you want from your site - the reason being people don't have much time - so you may get more help that way. I'm disappearing in a moment so here are some thoughts that come immediately to mind:
Have you used the Google Keywords Adwords tool? You might find some of the terms you want to rank for don't get enough traffic to bother with. It will also give you suggestions for other potential keywords: https://adwords.google.co.uk/select/KeywordToolExternal
On your website I'm unsure what the various menu options mean. I wouldn't have known "Noah's Minute" was a set of videos for example, if I hadn't seen you mention it above. The 'Family' and 'Mom MD' options on the menu - I don't know what they are. I say this as usability is very important for SEO. If people don't find what they're looking for on your site they'll go elsewhere - and a high bounce rate can have a negative effect on your rankings. So keep adding the great content, but find a way to organise it in a more user-friendly way.
Maybe (if you haven't already) you could get other parents to write guest blogs on your site about their own experiences. If they or friends have websites/blogs of their own, ask if they'll link to their own posts. In today's celebrity obsessed world, it might be worth seeing if you could get one or two involved - by writing a blog, if they have experience with children with down syndrome. It would be a good way to raise awareness and get more attention (therefore links, therefore increased rankings).
It would be a massive effort, but a great thing to do would be to make the best page on the internet for down syndrome information. Make it factual, with sources. Making something better than Wikipedia and the BBC is usually a good start (http://en.wikipedia.org/wiki/Down_syndrome / http://www.bbc.co.uk/health/physical_health/conditions/downssyndrome1.shtml). Perhaps it would be possible to do it in conjunction with a charity or organisation, who could verify what you've written (e,g, http://www.downs-syndrome.org.uk for here in the UK), or perhaps your personal experiences added to something like this would make it stand out over the more information-driven pieces. Maybe some down syndrome organisations could link to you anyway? See if they have links pages.
I hope that helps, sorry if I've been quick to the point on some things!