Illia is listed as a permanent follower according to UESP ( http://www.uesp.net/wiki/Skyrim:Followers#Permanent_Followers ), becoming available after you complete her quest.
The option to make her a follower after that quest may not appear in her dialog options if you have Hearthfire DLC installed. This is a known, UNpatched bug.
You may be able to get around that bug by reloading a save to sometime during her quest when she follows you, and then leaving the area with her and going to a Hearthfire house and asking her to be steward. If it works she will be bound to that house as it's steward, but will also have her options to be a follower put back in her dialog.
She can also be recruited into the Blades, which also lets her follow you.
With the Special Edition comes mods, and you may be able to find a follower mod that can help with your plan. Some current pc mods can turn almost any NPC at all into a permanent follower. Might be worth looking into when the time comes.