Is it the right time to start an online business with this economy?

Yes, it is the right time to start a business if you have something to sell that people want, or need, and will pay for. Things are tougher right now particularly if your business needs a loan or investment from outsiders, because both are harder to get during the recession. If you're planning to bootstrap it anyhow, there are a lot of deals available.

Business still goes on. Hundreds of thousands of businesses will start within the next 12 months, recession or not.

But you do have to do your homework, know what you're getting into, of course. Make sure you create a business plan. You need to know your core strategy, and by laying out assumptions into a plan you can figure out what you can reasonably expect to sell, for what level of expenses, and what the starting costs ought to be, and where you'll get the money.

Ultimately, your plan should answer this question for you much better than I have.