I'd say no. I got a puppy when i left a long term relationship which is hindsight wasn't the best idea. They're a huge long term commitment and I'm very fortunate I have an amazing family around me. If you have already given one up, I would have a very long time thinking about it. If you start a new relationship and want to go away for a wknd etc. You will be tied by the dog.
I did after I split with my ex (who also bullied me into rehoming my dog which ended up being one of the reasons we split). Since then I've got a second, they are great company and I couldn't be without them. I rarely go out though and when I do it can be a pain trying to sort someone to have them over night etc.