When performing to children, there are two ways that you can go:
1) You drop to their level and become a big kid, yourself. As long as you do this properly and do NOT condescend to them, they accept and love this kind of presentation.
2) You bring them up to your level and treat them as adults. As long as you're NOT condescending, they accept and love this kind of presentation also.
Either way you choose to go, the most important part is that you don't condescend to them...If you do, if you come across as condescending, they will eat you alive.
Personally, I choose #2 and, over the years, I've found that children, when treated as adults, will be more adult than adults themselves. Then again, I've been doing kids shows professionally for somewhere around 30 years.
You say that the birthday child is 6 years old. Well, at that age, I'd leave out card tricks altogether. And, by that, I mean the standard poker deck. However, if you are a creative individual, you can find animal cards on the market that you can use to show card magic with instead of using a standard deck. Color changes, for example: When a lion turns into a zebra, well, a six year old is going to react to such a thing and such a thing is going to be magic.
Get the idea?
Cups and balls...You've been doing magic for 3 months and you are preparing to get in front of the hardest audience in the world - children. Let me tell you, if you screw up, they're going to let you know. They don't have any problem with pointing out that you are hiding something in your hand if they see it and they're going to do it, right there, on the spot. Just how good are you at those cups and balls? How much study and time have you put into those things?
Here, have a look at Vernon on youtube:
http://www.youtube.com/watch?v=9JXILIWELt8&mode=related&search=
That is what cups and balls should look like. Are you capable of doing a cup and ball presentation that looks like that? That will work for kids at 6 years of age. Now, you don't have to be that good at it, but you had better be good because if you're not, those kids are going to eat you alive.
With kids, it's all in your presentation. You can do simple "self working" effects, like using a change bag or "Magician's Coloring Book" and go over a storm...But your presentation is what will make or break you.
At 6 years old, kids still believe in magic. This is one of the reasons that they will openly point out when they know you are doing something that you shouldn't be doing. They expect real magic, not some fake. And, they expect to have fun.
I can sit here and write you a book on this stuff. There is so much more than just getting in front of the group and doing tricks...
Thing is, if you have a copy of Wilson's you can put together an entire kids show that will work for you for the rest of your life. It's all presentation. It's all just having fun with those kids (whether you choose #1 or #2 above, it's still just having fun with them).
Now, this is not a paid for show (I assume, because at this point, you have no right to ask for any paid compensation for this). I suggest that you do it. The experience alone will be worth it. But, don't try to get 45 minutes in...If you can pull off a 20 minute show, then you'll be on your way. Again, look at what you can do with a deck of cards that is aimed at kids. Put a story together with it. A good story - take this seriously and don't give those kids a bullstuff show. Give them a show with magic and fun.
Look into the possibility of getting a pack of hat tears. Kids love the hat tear (and so do adults). This also leaves the birthday child with a souvenir of the show. Let me know and I'll PM you my presentation of the hat tear...But, I expect that you'll have several weeks to work it through - if you're doing the show in the next day or two, forget it. Like I said, give those kids what they deserve - a real magician. Please, whatever you do, don't give those kids a poorly put together show.
Now, I know that you're not going to come across as being a veteran of kids shows...Obviously. But, it is still up to you to ensure that you really are prepared. Even if you have a hard time with it (and you will), you can still walk off that stage feeling good that you've given them magic. That even though it may not have been the greatest magic show ever, they will still go to sleep that night believing that magic is real and have seen real magic earlier that day. You can do that. And that is what I expect of you.
Also, if it is a smallish group, you can do close up work, too. One of the fondest memories that I have was doing a magic show for 4 children. Sadly, that is all that showed up for the party for the birthday child...My heart went out to that little girl that day, when I saw the turn out and considered how she must have felt. I do believe that that is one of the best shows that I ever performed. I sat down cross-leg style on the floor, right there, only inches away from those kids and did my entire show in that format. I threw out my proper show and opted for close up effects that I was competent with. Things like Matrix and other money effects. Stuff that I could do, on the floor, for an audience of four. And those kids ate it up!

Like I said, I could write you a book, here...
Anyway, if you choose to do this (and I think you should), then do it up and do it right. Glitches will occur, problems will crop up. So what? Do it. Show those kids magic and that's all you have to do.
Mike.