Mr McVeigh has said he will formally resign from his state seat on April 29 to contest the federal seat of Groom in the upcoming election. He was preselected by the Liberal National Party to run in the seat, replacing Ian Macfarlane, who announced in February he was retiring from federal politics after 18 years.
The LNP has suggested the by-election be held on May 28.
Ms D’Ath said Mr McVeigh should quit now, not in a fortnight.
“It might suit the LNP to want to have a by-election in the middle of a federal election (but) it’s a bit of a distraction,” Ms D’Ath said.
“Is that in the best interest of the people of Toowoomba South?
“The question is why in two weeks, why has he not put his resignation in already if that decision has been made?”
Opposition Leader Lawrence Springborg said the last Saturday of May would be a reasonable date for a by-election.
“We’re giving the Government a way to deal with this matter expeditiously,” Mr Springborg said.
“So we very much look forward to the consideration of that by the Queensland Government. This is a respectful amount of time.
“What usually happens is that the Electoral Commission and the people of Queensland get no more than 26 days notice for a full general election.
“This of course provides significant notice which is almost twice that particular time frame.”
If a by-election was not held immediately in Queensland, the Opposition would have one less vote in the hung parliament, where the numbers are currently 42-all between the major parties.
Acting Premier Jackie Trad said the calling of a by-election was the prerogative of Annastacia Palaszczuk who was in China on a trade mission.
“The Premier comes back from on the weekend. She will have an assessment of the situation and will make a determination,” Ms Trad said.