I haven't personally had any ant problems up there and have camped in the area (Lake Elysia) several times.
I was up there for 5 days at the end of March last year & didn't see any in or around the area.
Lake Elysia is one of my favourite camp sites anywhere, the sunsets / reflections are pure magic in the right conditions.
There are several terrific areas on the western shore near where the track hits the lake, tho some can be damp.
One of my favourite spots is a little up the hill (50m or so) north of this point on a pineapple grass terrace with great views of the lake, The Acropolis & Mt. Geryon.
The day walks from a base camp here are fabulous (Walled Mtn, Macs Mtn., Upper Labyrinth area, Mt. Geryon North, Mt. Hyperion, Du Cane Range high point etc. etc.), tho it sounds like you may not have a great deal of time
Hope you get great weather up there Peter; a few pics from my Easter trip up there last year to inspire.
Cheers.
Stuart.