Are you wanting it displayed for users using quick fields interactively this way? Or do you only care when it's inside laserfiche?

There's two issues here. One is the space issue. To tackle that I usually use a regular expression of when I'm capturing by setting a token with the following: (\d\d?)/s?(\/)\s?(\d\d?)/s?(\/)\s?(\d\d\d?\d?) then applying that token to the date. This way it doesn't return leading or tailing spaces around the / symbol and it will accept a 1 or 2 digit date for month and day along with a 2-4 digit year. 

I actually also try to avoid actually filling out the date inside quick fields unless my data source is very clean, and instead let workflow try to set it based on a passed string token using date token caculator. (this is more important if using QF Agent)

EDIT: Matt Ross covered this part that I didn't know much better. 

For the leading 0 when it doesn't see it, I don't know of a way offhand to change that in quick fields. However internally inside laserfiche I don't think it includes a leading 0 either, it just displays or exports based on your field display format.