I disagree with Smitte21 and I would keep Charlotte on puppy food until she is a year old as she has a lot of growing to do. How heavy is she? Another thing you probably already know, is never to exercise a dog for an hour or more before, or after feeding!
I have to say that walking a puppy that is only five months old for 45 minutes is far too much, especially if you have been doing it for some time! She probably won't have let you know it was too long for her to be walking, until the damage had been done! Did your breeder or your vet not tell you that Basset Hounds have to be restricted in their walking time whilst young?
My family have had Bassets for many years and have never walked a puppy for more than a few minutes of gentle exercise on a lead (or better still, natural play in the garden when they choose how long to play) and to meet other dogs for socialisation, by driving pups to the local park or beach and sit on a bench and meet passing dogs or just a few minutes walking around on the grass.
Due to the terrific growth rate of young Basset Hounds there is a huge pressure on the puppies' ligaments, muscles and bone development, so it is recommended to avoid long walks with a puppy, especially under 6 months of age. With this in mind it might be worth carrying out the collar and lead training in the garden or a restricted place where the puppy isn't tempted to walk too far.
If you don't want to take Charlotte to the vet, if it was me, I would very much restrict her to the garden or a few minutes gentle exercise on a lead for three or four weeks and see how she does. If you take her to the vet, she will possibly be put onto Metacam or something like that and too much of that sort of stuff isn't good for them at such a young age!
Just my opinion of course, but from experience of two generations of my family owning Bassets!
Edit: Another thing is to not let Bassets go up and down stairs - going downstairs is particularly bad as the full weight of the dog (might be 65-75lbs when grown) is pushed onto the little front legs and can cause joint problems!