This is a matter of perspective, clearly, but that's not at all what casual means to me.
First of all the title (9/9 bronze) is very, very easy and could be done by your average 50k DPS LFR-hero. You get 45-60m to complete bronzes and the only way to fail is to wipe 8+ times. The mount is harder, but anyone who can handle flex or normal mode raids can easily get 9/9 silver without bothering with ideal group compositions, consumables or specialized CM gear.
Getting your transmog set will require a bit more effort for most people, but doesn't require a lot of the things people think it does. A player seeking 9/9 gold should have the following things: 1) a non-legendary meta gem, 2) a pair of good CM trinkets (463 blue trinkets are better than most SoO trinkets because of scaling), 3) consumables (flask, DPS potions, Klaxxi amber for healers, invisibility potions), 4) a steady, patient group to work through each run, 5) a good baseline understanding of class mechanics (you need to do about 60-80k single target DPS in 463-scaled gear).
Having previous experience with CMs, even sub-gold, will help. Having a tank who has done them before is worth his weight in gold. Some CM runs have taken me 3 hours to come away with a single gold, and some I have cleared 6 golds in the same time. Be patient, be prepared to wipe and learn. It can be done by anyone willing to put forth the effort, and that effort can be spread over multiple nights/weeks on a schedule that works for your group. My first 9/9 CM group was probably 6 weeks to complete.
You have plenty of time before WoD, so just start working toward the goal and you will get there.