How to check my partner to have sex without condoms?

Hi I am 24 and my partner is older than me and she has kids. She insists me to have sex without condoms, but i never did until now. I was scared all this time and now i told her we both have to be tested before we have progress in this relationship. Her reply was what all the test we need to undergo before we find out weather we have Sexual Transmitted Infections. Please advice me which clinic i have to go to in Melbourne