It's risky enough that if you have no other reason to go poking needles in there, it's preferable to wait. However, if there's other testing to be done (e.g. other genetic testing for potential prenatal treatments) then you can take the opportunity to test paternity.
Gralson: my husband (works out of town).
Auto: my girlfriend (lives with her husband Zoffee).
The most dangerous phrase in the English language is "we've always done it this way."