I am so sorry about your other dog.: He looks like he was a happy dog. Was it door darting that had your dog loose?
Maggie looks fantastic and very much at home! I am sorry that your loss was the reason for getting her, but am very glad she has a new home that will love her.
There are many methods to prevent the behavior, but you have to adjust to your situation. Here, we simply did not allow any dogs to approach the door, having a sit stay far back. Our one door rusher got locked in crate or room before we opened the door (or someone picked her up).
There are harsher methods... such as using a hard pizza box and having someone hide outside the door and smack them if they go out. Does it work? Yeah, but then you teach them fear of the door. People who have a garage door sometimes use it for a front door that opens on a busy street, content to have fear of that door firm since they have alternate door.
Other people set up a gate system on the inside of door so that the dog cannot get to the door... easy if it is an entry hall, not so easy otherwise.
I personally prefer more positive training. Here is an excellent article by Karen Pryor on the whys of door dashing desires and how to train against it:
And, as always, basic behavior training helps build relationships and confidence.