Hi,
Two possibilities:
1) get plastic cake containers, so you can re-use in the future: this can be bought from most Malls.
2) get paper disposible conntainers, in this case you can try to ask any pastery shop if the can sell you a couple or try to find them in one of the following shops ( Ramiz: several branches one is on Salwa road beside Elli France. or Rownaq ( one branch is in The center complex - Huge place - under ground) and maybe also Shaheen.
Hope that this info was of some use.
Don Not forget to add in the plates , Forks, cups napkins ...etc and the cake knife as suggested above ( I am sure you know: but it is a fine suggestion- and one does tend to forget somthing every time no matter how hard you prepare :-)
Please do Tell your Kid: Happy Birthday from us all here in QL