mevasui

Hey how's it going?  I saw your question first and then went searching for a cover up I'd seen a few weeks prior. Finally found it. 
In answer to your question:  I DON'T KNOW. I'm not an expert on tattoos and it looks as if you have a ton of color and detail in a tight space. However, I have seen lots of expert talent and skill on Instagram so....anything is possible?  But be willing to get in a waiting list and pay much dollars for what you want. That's a big if. That said, I would first find a GOOD artist before attacking your tattoo with a laser treatment or anything of the sort. You don't want to make things worse than it already is. 
Welcome to the forums and don't be afraid to try out the search function. I'm fairly new myself, so still learning the lay of the land. In the Photo Gallery is a section of covered up tattoos as well. Those aren't really great though. Lurk around the threads for the skillful artists and get your name on a waiting list. 
Again, it doesn't hurt to try. Well in this case it might. Best wishes!
 

Welcome to the forum! The key to answering your question is to find a good artist who is experienced in cover-ups. That's a critical piece - you need to find someone who has the ability to translate the existing work into somethin other than a dark mass of color. I would not recommend doing any laser treatments until you answer the question of whether a cover up is possible...and more importantly is it possible to cover with something you'll be happy with?
What is it that you don't like about your original design? It honestly doesn't look bad to me. The best ever - No. But it certainly isn't horrid. Do you have any ideas on what types of tattoos you might like? For anyone to give you recommendations it would help if you had some style in mind. Also, we'd all be taking a shot in the dark without some idea of what style(s) you like or don't like.
There is always the school of thought much espoused here to accept what you have and move on to the next. In other words, spend your money on new art, not trying to fix old art. Laser treatments are painful and expensive. That should be your very last resort, IMHO.
Where are you located? Are you willing to travel? Answering those questions will help the experts here provide some guidance. But, in the end, you are the one who has to be happy with the results.