It depends on whether your small business is using cash basis or accrual basis accounting. With cash basis you recognize income when received, so if you got paid in January 2019 that income would be reported on your 2019 tax return filed in 2020. With accrual basis accounting you recognize the income when it is earned, so income from a photo shoot in December, 2018 would be reported on your 2018 tax return.
Most small businesses use cash basis because it is significantly more simple. Once you pick a method you actually have to request approval from the IRS to change it (it's not an uncommon switch to make, but it can be complex).
The Earned Income Credit could certainly be affected, the income could result in more or less EIC based on where you fall between the thresholds for qualifying since EIC has both minimum and maximum income thresholds. For a photography business, cash-basis typically makes much more sense than accrual, I wouldn't suggest letting EIC impact affect how you choose to account for business income.