I've been to Iceland on Icelandair flights between NA & Europe most times I've flitted between those two continents. My advice would be to organise it separately on FI to your flight to a NA or Europe airport. I've not flown Iceland Express or Wow but usually the FI flights are around the same price anyway (or have been for me) and it is as full-service as you get to Iceland.
A travel agent pointed out that it was their favourite sector recommendation (in 2007 - when FI still issued paper tickets) and I've used them ever since. Iceland is a great place to spend a few days on transit - and the FI model is basically built on those stopovers. It has a reputation for being expensive but really is probably much cheaper than travelling in Oz (prices do go up in Summer, as do the crowds), and other expenses not so bad when compared to Oz prices (much cheaper than Norway!). My recommendation would be to hire a car and just drive and explore - the landscape is truly epic and unlike anything else on the planet, and the country is relatively compact. One of the nice things about hiring a car in Iceland is that they deliver it to you and pick it up from your hotel!
You should note though that many small towns (e.g. Hofn) won't have any accommodation in the winter months - have had to sleep in the car once or twice when caught unawares! Also be careful of wind warnings (these will be signed if appropriate). When they are up they mean them. An Australian staying at the same place I was last time didn't heed them and when he opened his car door the wind smashed it into the front of his car and it ultimately cost him about $5k. Wind along the south coast can quite literally pick a bus up. Areas like Jokulsarlon or Myvatn are easily accessible by road and you could drive around the whole island in a few days - you'll often get them to yourself if you're not with a tour group. I've done this 4 times and find new things each time. The ring road is pretty good for a small car, you would need a 4WD for internal roads, many of which aren't even marked - if you wouldn't be comfortable driving the remote red centre I wouldn't drive the remote Icelandic interior either.
Icelandair really don't do partnering, so your points will essentially be wasted. You could go with a non-FI airline, but they are usually far more expensive and far less frequent, and points aren't always guaranteed on those routes anyway. You should also be aware that KEF is about 50km from Reykjavik, and that no internal flights go from there (except a summer flight to Akuyeri that sometimes is available). You can get a coach ticket to the Reykjavik, and you can hop off at Blue Lagoon for a soak on the way and hop on a later bus to town. It's a nice way to relax after a long flight!
Excuse the lengthy post - I'm quite the Islenskaphile!