Do you like pencil skirts? Do you wear them? If you do, then go for it!
Both these items (top and skirt) actually look fairly classic, so I don't know if that is the issue, per se. I think there is a problem with the proportions of this outfit -- the length of the top seems to be wrong for the skirt's shape, and same for the jacket. And there also seems to be some dissonance in the details -- the sporty collar seems to compete with the slightly boho style of the earrings, and then the earrings and your glasses vie for attention, the jacket seems too "weighty" for the skirt and sandals and bare legs.
And then...the items aren't "inappropriate" in themselves...but they are sort of leaning in that direction, if you know what I mean. The skirt is relatively short (mind you, you can wear it really well!!) but combined with its fullness and bright colour it might read more like a weekend or even party skirt than a business skirt. The top, meanwhile, reads as a bit sporty, and might seem on the too casual side, especially with sandals.
I do think that modern classic items in bright colours is a foolproof business casual option -- as our own MaryK illustrates brilliantly every single day -- and today's featured blogger did as well. Actually, their jobs require a higher level of dressiness than yours from the sounds of it. But the idea is the same.
How about trying the top with charcoal or navy trousers (even denim), simpler earrings, and different footwear?
And the skirt, as suggested, with a tucked white top, or maybe with a semi-tucked knit in a colour of a different value (lighter or darker than the skirt) or with a neutral?
I do think these colours look great together and I do think they can be worn together in a business environment, but it might take some skill to make them work. And until you get the silhouettes that you like down pat, it might be easier to play around with them by mixing with neutrals.
Phew. I went on a lot longer than I expected there. Apologies for that.