formula to return lowest value in a range

Hi,

I am trying to set up a cell formula that looks in a range for all records that match a given text value (here, an animal type), and returns a blank if any associated records in the lookup range are blank, or return the latest date time value if no associated records are blank. There could be varying numbers of records associated with each text value.

Any help would be very much appreciated. Thank you in advance!
[TABLE="border: 1, cellpadding: 1, width: 500"]

[tr]

[td]

[TABLE="border: 0, cellpadding: 0, cellspacing: 0"]

[tr]

[TD="class: xl68, width: 80"]animal type

[/tr][/td][tr]

[TD="class: xl69, width: 106"]checkup date[/TD]
[TD="width: 35"] [/TD]
[TD="width: 64"] [/TD]
[TD="width: 216"]formula returns these values:[/TD]

[/tr]

[tr]

[TD="class: xl65"]dog[/TD]
[TD="class: xl71, align: right"]1/1/2017 16:46[/TD]

[td][/td]

[td]

dog

[/td]

[TD="class: xl72"] [/TD]

[/tr]

[tr]

[TD="class: xl66"]dog[/TD]
[TD="class: xl70, align: right"]1/2/2017 16:46[/TD]

[td][/td]

[td]

cat

[/td]

[TD="class: xl73, align: right"]3/4/2017 19:46[/TD]

[/tr]

[tr]

[TD="class: xl66"]dog[/TD]
[TD="class: xl70, align: right"]1/3/2017 16:46[/TD]

[td][/td]

[td]

fish

[/td]

[TD="class: xl74, align: right"]9/3/2017 13:22[/TD]

[/tr]

[tr]

[TD="class: xl66"]dog[/TD]
[TD="class: xl75"] [/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl66"]dog[/TD]
[TD="class: xl70, align: right"]1/5/2017 16:46[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl66"]cat[/TD]
[TD="class: xl70, align: right"]3/1/2017 16:46[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl66"]cat[/TD]
[TD="class: xl70, align: right"]3/2/2017 17:46[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl66"]cat[/TD]
[TD="class: xl70, align: right"]3/3/2017 20:46[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl66"]cat[/TD]
[TD="class: xl75, align: right"]3/4/2017 19:46[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl66"]fish[/TD]
[TD="class: xl70, align: right"]9/1/2017 13:22[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl66"]fish[/TD]
[TD="class: xl70, align: right"]9/2/2017 13:22[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[tr]

[TD="class: xl67"]fish[/TD]
[TD="class: xl75, align: right"]9/3/2017 13:22[/TD]

[td][/td]

[td][/td]

[td][/td]

[/tr]

[/TABLE]
[/TD]

[/tr]

[/TABLE]