She said on Election Day last year, 18,000 people cast special votes on election day, but their votes weren't counted because they weren't enrolled.
Haworth also called on the Government to change the law.
Data from the Electoral Commission showed almost half of all votes in last year's general election were cast early.
"It seems ridiculous now that we have about 50 per cent of people voting in the early voting period, but people can't enrol and vote on the day of the election," Haworth said.
"There is no real reason not to allow enrolment and voting on the same day," Haworth said.
The Electoral Commission Chairman Sir Hugh Williams agreed.
"When all the voting was on Election Day, you could understand [the current rules], but now with advance voting stretching back a couple of weeks before the election, it seems anomalous that that is still the position."
Williams said he wanted the law to be changed so people enrol on Election Day by 2023.
But Little said he was aiming for the 2020 Election.
"I have told the select committee that I have asked justice officials to have a look at that specifically."
But he worries that the select committee inquiry could go on too long, which could mean the rules would not be changed in time for 2020.
"If it looks like that's the case, then subject to the agreement with the rest of Government I would anticipate a law change by 2020."
The Electoral Commission also asked the Government to consider changing the rules around what happens when someone votes early but passes away before Election Day.
At the moment, if someone registers an early vote but dies before Election Day, that vote does not count.
Last year, 2300 people were removed from the electoral roll because they died during the advance voting period, the Electoral Commission said.
Williams said the Government had to change the electoral law for this to change so those votes do count.
But Little said there was no room for a law change in this area.
"Votes cast for an election, on a designated election day, should be people who are alive in my view."