Victorian Era is 1837–1901. Early period of film starts in 1890s. So is it possible to record and replay? Of course, because it was done.
For transmission, it is more complicated. First prototypes was mechanical:
As a 23-year-old German university student, Paul Julius Gottlieb Nipkow proposed and patented the Nipkow disk in 1884
As you can see, still very well in Victorian Era! Sadly, it wasn't practical then:
By the 1920s when amplification made television practical, Scottish inventor John Logie Baird employed the Nipkow disk in his prototype video systems.
So you need to stretch it a bit, and made electrical amplifiers available some 20~30 years earlier, or make your system use higher voltages - steampunk vibes for the win!
"The ability to record colour (any 'resolution')." Was not in the question when I was writing my answer. Still, with three disks and some color filters it shouldn't be that impossible.
Bonus: Audio
Again, looking at Wikipedia suggest that there were attempts during Victorian Era to make something like telephone.
Innocenzo Manzetti
Innocenzo Manzetti considered the idea of a telephone as early as 1844, and may have made one in 1864, as an enhancement to an automaton built by him in 1849.
Johann Philipp Reis
The Reis telephone was developed from 1857 on.
Given that telephone prototypes actually were built, we can be reasonably sure sound transmission is possible. Yet again, amplifiers would help.
