Your girlfriend is right, I'm afraid you'll have to go through with it. There's no threshold below which registration isn't required - as soon as you're selling regularly and with the intention to make a profit, that's formally a business, whether it's 50 euros or 5000 euros a month. The tax authorities take this pretty seriously, and with Etsy you're leaving a documented trail anyway. Better to register it yourself than deal with trouble later on.
The registration process is pretty straightforward: you go to the trade office in your city (or do it online, depending on how your municipality handles it), fill out a form, and pay a small fee - usually around 10-30 euros, depends on the federal state. After that you get your business registration and the tax office is automatically notified. Then you'll need to apply for a tax number and possibly register with the Chamber of Crafts, depending on what exactly you're making.
With 300-400 euros a month, this should be pretty relaxed for you - you write down your costs (materials, packaging, Etsy fees, etc.) and only pay taxes on the profit. As long as you're recording your income correctly, there shouldn't be any big surprises. I'd do it soon and not put it off, then you'll have it taken care of.