Assuming you're old enough, why not do it sooner? I know there's a school of thought to 'cutting your teeth' on a smaller cc bike for a while, and no doubt that works for some - but I personally see that as a waste of time and money. I jumped straight into DAS without ever riding a bike; it's all about respecting the bike and keeping your wrist in check.
No idea about your bike, but the 125s I rode during training, made every single aspect of riding harder. It was a night and day change getting onto the 500cc jobbies - you quickly tune into how much easier they ride, and get to really focus on improving your skills.
But, as with your tail tidy - it's always your choice, you may find that you love the 125 and will stay with it for many many years; even after passing your test. It's each to their own.
The thought of going straight through my test etc has certainly crossed my mind but with a second child due in Dec and the fact I use this to commute to work through villages and country roads makes a test and a bigger bike more of a want than need.
I feel mine is far easier to ride over the bike I did my CBT on but can't compare to a bigger 500cc+ bike.
But plan is to get a year under my belt, do my test then see if or when I get bored of a 125 then go from there