I didn't even wait to get to an empty office when I came out to my boss and a close colleague... I just burst into tears right in front of them! That was at a fairly emotional time, I didn't have any concrete plans on transitioning but I knew the lever for it had been thrown. 12 months later...
Anyway, you're going to be pretty much OK if you're working in Sydney, Australia (which I'm only presuming by your user name!!)...
I think it varies depending on the overall culture of the organisation and the nature of the people working there. Sounds like you're in a large workplace so it's likely you'll encounter "resistance" from some quarters - by that I mean, blokey bros and uptight TERFs and probably a few hardcore religious types.
NSW workplace laws protect you from discrimination and harassment on gender identity grounds and your employer sounds like they are across that. Thing is though, although people have to treat you with a degree of respect that doesn't mean they have to like you. You might encounter passive aggressive resistance (eg deliberate misgendering and dead naming) and could shoulders (ignoring you or moving tables) from some and plain idiotic behaviour from others (asking supposedly "harmless" questions or making outright stupid statements). Keep a journal of all that of behaviour, record who, where, when, what - keep it impersonal and emotion free. If you have ally's have them verify it. And report it. Don't presume idiots and bullies will change their way, if they think they can get away with it and nothing happens then they will only get worse. It's up to you're employer to provide a safe workplace for you and to put the others making life difficult for you in their place.
All that said, I didn't have any of those issues in my work place. But it was much smaller (only 15 employees), very progressive and community based and largely women, so there wasn't a macho or blokey culture anyway. That made it a lot easier. I actually told everyone in a staff meeting. Our organisation did have a big community footprint though and we had connections with many others outside the office, those people were told by email by my CEO based on something I had written. I was amazed at the flood of support I received from so many people.
I am also a wig wearer, and honestly I got nothing but genuine compliments. Just pick something that looks natural and suits your complexion and style and people will either not realise or quickly forget.
I think the bottom line is that if people respect you and like you already that won't change. Just be confident in who you are and your presentation. If they see that transition has helped you finally be true to yourself and made you happier they with get right behind you.
What's your timeline?