Hi there! Congratulations and a warm welcome to the forums! Your little one is four and a half weeks old so a couple more weeks would be nice and fully weaned would be even better but life isn't always perfect. The good news is healthy baby quakers are very hardy little birds and with a few precautions your baby should be fine. The first few feedings are awkward for the baby and for you, both of you will get comfortable in no time.
A few things to keep in mind. Keep everything around the baby as clean as possible, especially the feeding equipment. Baby birds are susceptible to bacterial crop infections. Mix only enough formula for one feeding and throw the remainder away after each meal. Never warm the formula in a microwave, formula can overheat easily, the formula will not heat consistently and a hot spot can cause crop burns. Mix the formula according to instructions and feed at the temperature suggested for the age of the bird. Keep a warm wet cloth to wipe the formula off the feathers at every feeding. It's better to put the baby in his cage and leave him alone for an hour after you feed him to give him enough time to quietly digest his meal. It's important that the crop empty completely after each feeding. Keep a fresh supply of water available and you can start offering your choice of pellets and a little fresh food, quinoa, brown rice, finely chopped kale, grated carrots, cooked peas, oatmeal, etc, he or she should start to show interest in the other foods at about six weeks. There are several organic baby food brands that your baby will probably like, you can warm the baby food and feed it from a spoon. Your baby will eat ravenously for you at some feedings and not so much at others, don't force feed, if he doesn't want to eat wait an hour or so and try again, if he begs it's okay to feed him. He should be alert and curious but he's a baby and still needs more rest and quiet time than adult birds. I hope that helps. If you have questions or concerns please let us know, we have members that have fed younger chicks. Best of luck, looking forward to photos!