My name is ***** ***** I’ve been involved professionally with dogs in the health and behavioral fields for over 18 years. It will be my pleasure to work with you today. I think you hinted at the answer yourself. She gets excited and urinates as a result. It is actually referred to as excitement or submissive urination as it occurs when dogs get real excite or are being submissive. Perhaps the long fibers feel good as she walks through it, or perhaps it feels like grass to her. She is also only 4 months old and probably not totally house trained yet.
They actually make medications to help strengthen the bladder sphincter which tends to help keep the urine in when they are excited. You can try behavior modification to try and eliminate this problem though it is harder when it is excitement rather than submissive in nature. You can read of some techniques here.
There are medications which I touched on above that have been found to be effective for this problem and you should ask your Vet about Proin for dogs over 6 months and Imipramine for those younger. It is likely she displays some submissive urination as well or will. In many cases, they will roll over, showing their belly and urinate a little. I've found that obedience training gives dogs self confidence and helps cure this problem when related to submissive or fear urination.
You might help the situation by putting a diaper on her and walking her on the shag carpet more so she becomes more familiar with the feel and texture. If she becomes used to it, she won't get so excited. You might combine it with the medication to ensure the carpet does not get soiled with urine drops.
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Since there have been recalls on certain foods, please check the following site to be sure the food your animals eat is not affected. If it is affected, contact your vet as soon as possible. Have your dog seen if they have any symptoms.