There may be a dust issue, but if you're willing to clean your case and take care of it it'll be fine.
What if I don't want to clean my case? I am way too lazy for that lol
You can get a case with dust filters and keep it off the ground, then. x)
If you don't want to feed the dog then why did you get it?
Whether you wanted it or not, Your parents gave you a chore, So do it. Why should you be getting things like food and shelter for free? You gotta earn your keep somehow.
where is your PSU located in your case?
If its on the bottom, then which way is the air intake for the PSU oriented? Up or down?
If its down, then put a board or some other hard smooth surface under the PC so you're not blocking the airflow to the PSU with the carpet.