Yep, it's totally possible and you can transfer at the end of first or second year (and possibly mid year if USYD offer mid year entry to Economics). If you transfer courses you just apply for an internal credit transfer and they'll give you credit for all your completed units. BUT I should point out that graduating with a BA in Economics is - subject-wise - no different to graduating with a Bachelor of Economics! The only difference is, in the B Economics, you can major in Financial Economics (although the units you do to make up this major are units you can do in a BA as part of your Economics major anyway).
A BA requires an ATAR ~80 to get in, whereas Economics is closer to 90. This means that if you got an ATAR in the low to mid 80's you'd realistically need to be looking at a Distinction level GPA to transfer into Economics. My experiences with the faculty of Economics at USYD have shown me that this is not necessarily easy, unless you're someone who really loves maths
Another (slightly unrelated!) piece of advice here: if you have an interest in Economics, do a double major in Economics and Political Economy - the Political Economy department at USYD is outstanding and gives you a much better grounding in practically applicable economic theory than the "School of Economics" does. Economics at USYD is extremely maths heavy and a lot of it is very, very boring! If you're someone who enjoyed economics in high school, Political Economy is more likely to be up your alley. Also, when you graduate, a double major in Economics/Political Economy shows you have both the quantitative and qualitative skills to work in advisory or consulting positions, if that's what you're looking to get into.
