In Australia I will need a lot of budget because I have to buy many things.

First of all budget is countable, and since you've written 'a lot of', then there should be an 's' on budget. But there's another problem. Budget has 2 meanings that are potentially useful in this situation:

1. Budget - Sum of money

Budget as a sum of money that has been set aside for a particular purpose:

In Australia I will need a large budget because I have to buy many things.

2. Budget - Document

Budget as a document containingĀ a list of items:

In Australia there will be many items on my budget, and so I will need a lot of money.

In both of these examples..

  • budget is a singular countable noun
  • large collocates with1 budget
  • item(s) collocates with budget
  • as a singular countable noun, budget requires some kind of determiner (article, possessive, etc.)

Often students who are preparing for IELTS feel they have to do everything to avoid repetition, and so they useĀ budget instead of money. However, budget is not synonymous with money. When you're talking about money and comparing how much things cost, it's safer to use words like money, cheap, expensive, etc.

1Collocation is explained in a separate post.