Dating is something that you should want to do. Not something you feel you should do because someone is asking you to.
go for it!! Dating is one of the best parts of being single! Dont feel like you need to settle down with one person so fast. Enjoy!
If you're ready, go for it. There's no official rule against it ;)
if you want but there's nothing wrong with being single for 2 months. especially 'cos youve come out of a long-ish relationship, so you might just want you time. :)