Hello Tanya,
Firstly,you are targeting a very competitive keyword right away, I'd have started off by targeting a e-learning related keyword that has lower competition and after I got decent rankings for those keywords, would have moved on to the competitive ones.
Secondly, you need more keyword rich content on your site. Buying a subdomain sounds like a good idea for adding content. As such the subdomain will not hurt the main site, but have chances to rank better than it if it has more content and links

Put the best articles there and publish all other articles in major article sites like ezinearticles.com etc. Place a link to your main site URL with your targeted keyword in the author bio section.
As your site's homepage lacks textual content, you have to compensate that through backlinks. Run a full time backlink building campaign and be sure to use variations in your anchor texts.
Also I believe I should warn you against the Google sandbox. As you have a new site and it is trying to rank for a very competitive keyword, chances are there to get into the Google sandbox.
Do the following to dodge the sandbox.
1. Use variations in your backlink anchor texts.
2. Place a couple of links to other related authority sites from your site.
3. Build links slowly.