Gearbox giving trouble, have car 3 months

Bought a 151 Peugeot 5008 semi automatic in August from a garage. There was 159 k km. Already, have had a starter replaced, air flow meter and had something reset as it wouldn't come out of 1st gear after taking off. In the past few days, if I'm stopped in traffic, going uphill, it seems like it will hardly take off and there's a rattle underneath. It is also slow changing from 3rd to 4th gear..I'm over an hour from the garage so it's hard to get there and back with work. Going on Saturday to check it out. If it is the gearbox and it is only starting to give trouble now, am I entitled to get them to replace it? Just sick of it now.