You should be fine, but get in touch with a local lender and meet with him/her to get pre qualified (no obligation to do that) so that you know exactly what you can expect to get for a loan and monthly payment with your PITI included.
I've done mortgages where people were on unemployment, graduating from college, changing careers etc. They key is: Do you have a regular base salary (W-2 income)? I suspect the answer here is "Yes"
The only time length of employment becomes an issue is if you are an hourly employee and your hours vary, your job is part time, you will be using overtime or bonus/commission income to qualify and so on.
One word of caution: Do not expect to close if you are between jobs. make sure you seamlessly go from one to the next. If you are transitioning, your lender will require at least one paystub from your new job in most cases. (Don't take a few weeks off before starting the new job if you have a closing pending !!!)
(Residential Home Funding)