1. You might be feeding too much. Too much in = faster transit time to make room for the next meal, & results in a loosely formed stool. You say you are feeding according to the bag - but this is just an estimate, & some dogs need much more or less than this amount. Better way to feed is to evaluate their condition. Check with your breeder to find out what your puppy should look & feel like as she matures. Also, puppies this age should be fed at least 3 times a day, so that they aren’t trying to eat too much at one time.
2. The gas is a bit concerning, and often formed by their inability to process one or more grain products. While many people will say “go grain free!!” it’s not usually necessary, and there are many products available that have alternatives. Corn is usually a #1 culprit, and I see that corn meal is the 2nd ingredient in your food. Looking for a product that has brown rice, oatmeal, or potato might eliminate the gas.
3. The protein source doesn’t necessarily cause any of the symptoms that you describe, but some are richer than others, & some are gentler on the stomach than others. Back in time when there were only a few options, lamb & rice was the “go to” food to be gentler on the system, but now there are many exotic mixes, including venison, fish & duck. I wouldn’t worry about the protein source at this time - if you decide to switch foods, sticking with a chicken protein (what you are feeding now) helps to limit the changes & narrow down what the issue really is.
4. There are some things you can add or supplement to help with the gas & stool as well, before you change food, or even with a change. First - canned pumpkin (NOT pumpkin pie filling) helps to add bulk to the food, & increase the ability to form firm stools. Green beans (if canned, buy “no salt added”) are great for adding bulk to help their bellies feel fuller, without contributing calories that might result in unwanted weight gain.
5. Yogurt added to food (plain or vanilla - NO artificial sweeteners!!) or probiotic capsules (acidophilus, lactobacillus) can help increase the natural gut bacteria to digest their food. You could even try this without changing the food & see if it helps - treat for 3-4 days & if there is improvement, continue for 2-4 weeks before trying to wean off.
6. Are you feeding treats? Treats & edible bones can be like junk food for dogs - richer, higher calorie, & remember it contributes to the overall food intake. Reduce treats until you get the diet under control.
If you change foods, do it over 2 or 3 days. Day 1 = 2/3 current food, 1/3 new food. Day 2 = 1/3 current food, 2/3 new food. Day 3 = all new food. Also, start by feeding the same total amount each day, and check the puppy’ weight in 1 - 2 weeks to make sure they aren’t gaining or losing too much; adjust as needed.
Look for a limited ingredient food - I recently put one of my dogs on Natural Balance ($53/30#) to resolve an allergy, but there are many other options. They do NOT have to break the bank, but keep in mind a higher quality food might cost more than what you are currently feeding. It doesn’t sound like you need to go “grain free” right now, just try to find something without corn to start with.
I hope this information is helpful for you - I’ve been breeding/showing/consulting on dogs for the last 17 years, so there’s been a lot of trial & error on my part, & collaborating with other breeders & vets on many cases during that time. If you have any additional questions, feel free to send me a private message. T. :)