Unfortunately a visa application I made was rejected leaving me with insufficient time to reapply for a temporary work permit, so I do not have personal experience of the journey but Google Maps has the distance as about 25 km. A Lagos Airport site has:
Traveling by taxi is also the easiest and the safest way transport in Nigeria.
Yellow taxis are the most trusted in Murtala Mohammed International Airport but always check driver’s ID, standard rates on the drives tariff card and ask for the price.
Note the distance from Lagos airport to City of Lagos is around 22 kilometers so you should pay around NGN 5000 (32 USD) for 30 – 60 minutes of journey.
Duration to Victoria Island will depend upon the time of day but may exceed one hour.
However, the easiest and the safest way is not necessarily easy or safe according to normal standards (eg see TripAdvisor).
Options include a pre-booked taxi or limousine for ~$38 - ~$216.
It seems that for the Lagos area professional drivers now require LASDRI certification - thank goodness, since driving licences can be obtained with no practical test of learner drivers (!). This is a card with photo, so might be deemed adequate official identification. However, there are many other forms of certification (as mentioned and imaged in the link) eg:
NATIONAL DRIVER LICENCE
NATIONAL CERTIFICATE OF ROAD WORTHINESS
MOTOR VEHICLE INSURANCE
and the author does mention Haven outlined these documents, having them always in your cars is very ideal so these may be to hand when seeking to hire a taxi in Lagos.