The DR is probably a 50mph bike. Yes, you’ll get more out of it in some situations but I wouldn’t expect you to maintain much more than that as a cruising speed.
My (admittedly limited) experience is that Learner legal 125s are just not A road bikes. You’re having to ride them “balls to the wall” to make them keep up with the traffic.
I had the DR for about 3 months and put 1300 miles on it before doing my A licence. I had thought I’d use it to get around the county but in the end it was mainly used to practice what are arguably the more important bits of the A licence – slow speed handling and the procedures (positioning, lifesavers etc.)
You’ll pretty much recover your outlay on a 125 and it will probably work out cheaper than extra lessons/retests if you fail first time.
Get the A licence done then find something that’s good for the commute.
Rich.