I was a postulant and novice in a contemplative monastery for two years. The director of postulants was a convert. From what I knew of her vocation, she entered the monastery fairly soon after her conversion.
I don’t know about official waiting periods, but I do know there are things you can do now as a part of your vocation. You can join the third order of your particular order if there is one. You can spend your days in service to Christ by serving the poor. You can attend daily mass, pray the divine office, and see where else God leads you.
A vocation does not begin only when you enter the physical house of your order – though there is NOTHING like that moment!. Although you cannot live out the fullness of your vocation now (any more than I can fully live out the married life without a husband!), you are already exactly where God wants you.
And everything the other posters here have said is right on the money. Talk to your pastor, get direction, take that direction, and pray, pray, pray.
Blessings.
Gert