We have a doggy door and I love it. Makes life soooo much easier with 3 dogs, and fosters always rotating in and out. I also have a medium door, and my dogs are 15, 16 and 18 lbs. They are in and out of it all the time, and I think it also improves their quality of life because they have free access to the outside.
When I adopted Misty, it was pretty obvious she had been trained to piddle pads, as she was absolutely convinced bathroom rugs were the place to go. If I took the rugs up, she went on the floor where they were, if I closed the doors, she went in front of the bathroom door. Pretty entrenched habit, and I don't use piddle pads, so we had a task!
She learned to use the doggy door right away and it helped a lot with housebreaking, as she would follow the other two out when they went and got the idea pretty quickly. I also did "housebreaking 101" with her and walked her outside a lot. Now, I have replaced my bathroom rugs, can leave the doors open, and she is fine
There are safety concerns with doggy doors, but I think it is a matter of weighing all the risks and benefits. I have a secure fenced yard, and live on a dead end street in a quiet, safe area. I once audio taped my dogs when I went to work (yes I know- a little crazy!) and found that they never even went outside when I was gone...was kind of what I suspected. But the door is there if they need it, and it is usually only a few hours someone is gone.
I do not let a foster dog, or a newly adopted dog, use the door when I am not home, until they have been with me a while and I really know their behavior. Most of the fosters I have never get to use it unsupervised because they might be flight risks, or have other issues.... and keeping them safe is priority. But there have been a few I have felt OK with.
Even with a secure fence, some dogs will dig under, or bark non stop when you are not home. I don't believe Havanese are big diggers though. So, knowing your dog is a big part of this. Some people will not allow their dogs to use the door when they are not there to supervise; I think you have to find your own comfort level with this.
On the other hand, I have thought that if there ever was fire, my dogs would be able to get out
I highly recommend a doggy door- you'll love it once you have it!