Having my wedding the same month as a friends wedding

I recently got engaged. My fiancée and I have always thought we would get eloped on a trip to Australia , we’ve been planning for a while now but when we broke that news to family, we were met with very heartbroken reactions. After researching elopements, we realized it would be harder to do with our budget and was harder to plan than we had originally thought. Eventually decided to have a small wedding and use this trip for our honeymoon. We want to have an outdoor backyard wedding with just immediate family and a few close friends. Due to being outside, we want to have it in summer time. However, we have a friend’s wedding that had already been planned for the same month. They are having a much bigger somewhat destination wedding. I expressed there would be nothing changing and I would attended her wedding and still fully there celebrate them. I also explained the limited date options we had to choose from and how I felt having a wedding after hers was the most respectful option out of all of them. There is no overlap of people attending our weddings besides my 1 friend who happens to be the sister of the other bride.