Assuming you have no checked luggage, it would be possible to meet at air side of T1.

However as m3red posted, T1 immigration can get very congested. If your wife is travelling in biz or first, you may not need to wait too long at land side if you need to collect your bags at T3 land side.

I guess this must be the first time your wife is in Dubai, hence wanting to meet her at the airport. If not (or if she is comfortable with it), then meeting at the hotel would be a better option.