For flights within EU have seen requirement is to have less than 8kg or even 6kg for dog + carrier. Other than a soft-sided carrier which is needed for the flights, outside flying time I can also recommend a travel backbag like this. when we brought ours, we had 2 flights, then we also took the train from Copenhagen to Malmo, felt she was more comfortable in the backpack tbh.
Like this one? Kurgo Dog Carrier Backpack for Small Pets, K9 Rucksack, Heather Grey, Waterproof Bottom for Pets up to 11 kg, Small https://www.amazon.co.uk/dp/B07QNZFWHL/ref=cm_sw_r_cp_api_glt_fabc_DQRM0RY049ET0AVDMWE4