“When should I start planning?”

The first key to having a stress-free party planning experience is to start the planning far in advance of the party date.

You may need a month or more to plan a stress-free party, depending on how difficult it is to plan the party

Although a children's party should be nowhere near as complicated as a wedding, you should probably start your planning about a month from the party date. That way you'll have plenty of time to make it as special as you want it to be without killing yourself to get it all done.
In addition, having a little more time to prepare will allow you to buy special items, decorations, favors, etc. and you'll also have plenty of time to make things for the party if you choose.
That means that your chosen party day should be at least a month away from now.
If you have at least two weeks (okay maybe one and a half might squeeze out a good one, then you can still make it work, but you're going to have to hurry and get those invitations out in the next couple of days.

If you have less than two weeks to get this party put together, I highly suggest that you move the date of the party back. Less than two weeks to plan a successful party just isn't enough time. In fact, you won't even be able to get your invitations out and get those RSVP's in time to know who will be able to attend.

Putting a party together at the last minute puts a lot of stress on you and puts your guests out as well. But if you are running out of time and you still want a good one, you may actually take the pain of calling them up one at a time and say that I’ll send you an invitation anyway. Sometimes that can make your guests feel important. It feels more personal.

But avoid last minute actions if you don’t like the hassle. In fact, what’s most hassle free, is to hire a kid (teenager – maybe even your own if you have one) who is having his school break to call and send out the invitations, perhaps offer him 2 bucks (or more if you’re feeling rich) for every person he calls. Give him half the money when he reports job done but don’t give him the rest until the party is over. This will motivate him to do a good job and not pretend that he has called a particular someone, even though he has not.

Once you've chosen a date for your party, the next step will be choosing a theme for your party.