This is my first foray into Homebrew stuff, I currently have a Tabaxi Bard from the School of Dance and I've been given the go ahead from my DM to create a weapon for her. My idea is a weapon that when inactive looks like the coin belt a belly dancer wears but by using a spell slot it activates to become a pair of Chakrams at the magic item level of the spell slot.

So at level 5 she can use a level 1 spell slot and it becomes a +1 Chakram. At level 10 she can use a second level spell slot for a +2 etc.

I've been trying to figure out how to do this in the homebrew section and not had much sucess. Can anyone help?

Did you get permission to create a “weapon” or a “magic item?” Because what you’re describing would definitely fall under magic item territory. Magic items aren’t really designed to “improve” like that in D&D, and since the rules don’t cover it the system isn’t designed to create them. If it were me I would skip spending a spell slot and switch it to a bonus action command word to just activate them as +1 weapons and leave it at that. If you want them to later be +2 weapons then you would either need to find some magic means of improving their enchantment (also not really covered under the rules), create a set of +2 versions from scratch, or locate some. The same would go for any +3 versions.

Would it be possible to create it as a cantrip which would automatically improve with levels?

Go through custom Feats to add it to your character with the material component requirement being the belt. 

Not the same thing I know but at least it can be coded with DDB.