I don't think you should feel guilt at all. My theory is your old pet sends you the new one. I have no scientific proof of this, but have seen it happen too many times. Pet lives are short and the grief is awful,but too many pets are waiting for a home.
Your old doggy was weary and needed her final rest. While she was jealous in life,her main aim was to see you happy and along come the newbie without even looking. You have room in your heart for both.
I miss my darling Ginger still,but King has enriched my life just as she did. His owner dumped him in a kill shelter which sounds heartless,but I am grateful she did. That dog makes me laugh every day,just like Ginger.