It depends on the impact to your business goals of not being full time.
If you can both do this part time until it starts paying well, then you're in a much safer position and you're still getting there. Waiting until you can afford to transition is a lot less stressful on you and on the business relationship ... but it doesn't always work that way.
On the tech side, if you're happy that your current pace is going to hit the March goal and there isn't much benefit then wait till it launches.
You will then see, once you have launched, what all the extras are you will need to do in order to keep your first users happy. Depending on how fast you grow this may still be a part time role, or you might need 3 more developers in order to keep up.
On the business side, if your revenue model is automated and your growth is around online advertising then your business partner may be able to monitor this from work or after hours safely. If on the other hand you need to knock on doors, setup meetings, do lots of presentations, go out and meet lots of prospective users and business partners then you should consider starting this process before the launch so that you have enough of a buzz going for when the actual launch happens.
Few suggestions to help you work it out.
Put up a simple "this is the concept, submit your email address if you're interested to see the launch" landing page for now. This will help you gauge the answers to the above questions. You could extend this basic site to have a "what are the key features you would like to see" survey as they submit (but no more than 10 questions or you will loose people).
Sit down with Excel and between you play forward a best case and minimum case senario month by month or quarter by quarter over the next 2 years. Run a few columns for income, employees, users signed up, users lost, features, marketing budget and see where you end up.