Since most pre-approvals are good for 6 months, it's not too early to get one. Figure it will take you about a month to find a place, then 60-90 days to closing. Speak to a few mortgage brokers/banks to first discuss what mortgage will be best for you based on preliminary information about your employment, income, debt, and down payment amount, then get that pre-approval. You will then know what you can afford.
In reality if you find a place by end of March, you could move by June or depending on the sellers cooperation, ask to wait till July (or close in June, just stay in your rental place till end of July and move in slowly into your new home).
If I can be of any help finding you listings once you get pre-approved, feel free to contact me via email or give me a call.