Definitely. The short trips is probably what kills a lot of modern diesels - people don't realise about the emission systems and how the engines need to be at full temperature to do it's stuff. I even used to hate 'shuffling' our petrol cars on/off the drive, so the van goes in 'first' and generally sits there all week. We use it for longer journeys.
The SCR (ad-blue) is a bit of a ticking time bomb, which is why I use Wynns additive to stop crystallisation of the ruddy stuff.
Doing short journeys isn't really a problem, so long as you also do fairly frequent longer ones.
I will quite often drive the 2-3 miles to Cowbridge or Pontyclun and back, but I also do a 40 mile drive to Swansea and back almost every week, half of which is motorway, and a reasonable number of other longer journeys, and I've never had an issue with the DPF.
Though having said that mine is (just!) prior to AdBlue, being a 2015 model, so I don't know how much that would affect it if it were needed.