I am certain you could take your boat to Little Barrier and back from Leigh.
But I would like to hear of your own experience on that trip.
Have you been out on other boats to Little Barrier?
Were they similar to yours or larger?
Do you have any fishing mates who regularly do the trip?
What safety equipment do you carry?
A VHF and Coastguard membership is a minimum requirement in my book
If you have no experience:
I suggest doing the trip a few times as crew with a local experienced boatie.
For your first few trips do it with another boat - two is company and nearby help if you need it.
Read the weather signs, most important out there.
Especially if a Westerly wind kicks in. It can get very gnarly very quick.
Good seamanship is being able to call it a day and head home early.
Just remember this if you have a problem out there, you will need to wait 1 hour plus before Coastguard will get out there to pick you up.
The picture below is departing Little Barrier for Kawau Island in a 9.4 diesel metre launch at 9 knots. The wind is westerly blowing about 20 knots very soon after this it was 30+. A rough trip home. When we arrived it was flat as a pancake.