Most couples of course plan their wedding much earlier and are keen to book their celebrant well in advance, especially if they are marrying on a busy Saturday in summer or a popular date like Valentine's Day. Wedding planning is an important part of the preparation for your life together as a married couple and working with your celebrant over a period of time to design your ideal ceremony is part of the fun.
There are some very limited circumstances where the Notice period can be shortened to less than one month. In situations such as terminal illness, immediate overseas postings and similar cases it is possible to obtain permission for an earlier wedding. Your celebrant will be able to tell you about these rules how to go about seeking permission.
So don't be fooled into thinking that you can call up your celebrant for a wedding in the morning because you have just met the new love of your life. It just doesn't happen like that.
Of course, if you are so madly in love that you cannot wait a month to gather your family and friends around you and declare your love to the world, you can ask your celebrant to do a "commitment ceremony" - this is what you saw on TV. These ceremonies have absolutely no legal basis and the celebrant makes this clear to everyone present. Later on, if you both decide you want to marry then you can return to your celebrant, give due notice and have a legal wedding - as large or small as you wish.