Essentially, I want to gain expertise in 2 skills but without having to take a level in Rogue (Or several in Bard)
There are already feats to gain proficiency in various skills/weapons, but I can't find anything (apart from a human-only from Xanathar's guide) that grants you the double proficiency.
So I figure making this a feat could work. But, I fear my lack of experience in home brewing things means this could be under/overpowered.
Is 2x proficiency on 2 skills OP? Bearing in mind this is instead of a stat boost – which would give a +1 to all skills in a category, whereas I want to be extra at something specific.
Balanced to core material, but depends on the campaign
In non-playtest material, there is the feat you mentioned yourself, Prodigy (in Xanathar's Guide to Everything, D&D Beyond link) that grants the character one skill proficiency, one tool proficiency and one new language, in addition to expertise with one skill (either a pre-existing one or the new one from this feat). Your suggested feat essentially forgoes the additional skill proficiency, tool proficiency and language proficiency in favor of having a second skill for expertise - seems like a fair trade to me. Your feat is in line with existing material.
However, whether Prodigy itself is balanced greatly depends on the role of skill checks in your campaign. How much a single check can accomplish is quite heavily at the GM's discretion, and so varies a lot from table to table as well as between situations. Before picking Prodigy or homebrewing another feat that grants skills or expertise, consider whether the campaign you're playing offers ample opportunities to use the bonuses granted by these feats. If not, you'll find both rather underpowered, possibly completely useless.