Do some experiments using the above guidance and see. Most likely, it will be more difficult, or the background blur effect won’t be as strong. You won’t be able to get photos with the soft backgrounds like I have with my 135mm on an iphone. It’s just not going to happen. Of course you can use portrait mode, but it does have some issues especially with the furry ears of long-haired dogs, because it’s an artificial blur and relies on the phone’s technology to recognise what is the subject, and what is the background.
It’s also possible to blur the background in editing, but in my opinion and experience, this is VERY difficult to do in a way that appears believable and realistic, because of the way depth of field operates – it’s hard to mimic without some effort. There are probably apps out there which may be able to do it, again they will rely on being able to distinguish the subject from the background and blur only the background.
In my opinion, if you have a phone, your best bet is probably going to be using portrait mode. There is SOME depth of field if you get close enough to the dog, and some phones’ portrait modes and DOF will be better than others.
If you have a camera, I would seriously recommend investing in a lens with a wide aperture (f/2.8 or smaller f/ number), and a mid to long length. Make sure you check out the “Choosing a Lens” lesson for more information. A good quality lens, with a wide aperture, can do wonders for your photography, as it can achieve effects that other cheaper lenses just can’t due to their construction.