Life is a (personal) journey.
In the U.S. it's no longer customary to get permission from the father prior to proposing to the daughter. In fact some women consider it sexist. Many women would prefer to be "the first" to know.
Having said that you know your girlfriend better than anyone else.
To tell you the truth when it comes to most marriage proposals they are usually not a complete "surprise".
Most couples have already had discussions about getting married one day, having children. and building a life together. Essentially both parties are in agreement that they are right for one another.
If you haven't shared those dreams together in prior conversations you might be setting yourself up for a rejection.
You don't want to be one of those guys who springs a proposal on a woman "out of the blue" especially in front of family/friends, or god forbid a public venue.
Oftentimes guys who do this are trying to manipulate a woman into saying "yes" rather than look like a cold hearted "b*tch".
Some guys like to chose a spot that is "special" for the couple. Maybe it's where they had their first date or at a picnic under a tree or while on a weekend getaway or romantic vacation ...etc
One of the best places to propose is in the privacy of your home. Maybe you've made a surprise breakfast in bed for her, placed a rose on the tray, with a wrapped gift box. When she opens the box instead of there being a gift or a ring there's note saying "Will you marry me..." or you could have a ring in the box and drop on one knee along the beside and propose.
Many couples actually enjoy shopping together for a ring.